Questions tagged [operators]

Questions about using or composing operators--functional mappings from one state or vector space to another.

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How to give a property to a list of functions?

For example, I have defined a bunch of binary functions Sum1, Sum2, Prod1, ...
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2 votes
1 answer
64 views

Visualizing order of operations

TreeForm[HoldForm[ (9-2^2+10 8)/9]] produces this: Is there a way to use Divide instead of ...
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  • 398
2 votes
2 answers
70 views

Product of different differential operators

I need to define a multivariable differential equation of the type $$ \mathcal{D}=\Theta_1^2-z_1(-\Theta_1+\Theta_2+\Theta_3+\Theta_4)(1+\Theta_1+\Theta_2+\Theta_3+\Theta_4)\\ \;\;\;\;\;\;\;\;\;\;\;\;\...
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  • 21
0 votes
1 answer
29 views

Confusing abnormalities observed when counting a specific operator in an expression [duplicate]

Recently I have met with some confusing abnormalities when trying to determine if there is a specific operator (usually Plus[] ) in an expression by programming. ...
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  • 383
2 votes
1 answer
73 views

How to convert an expression of several variables into an operator

Given the expression How can I define the following operator like g[u_, v_] := eq1 The correct definition is
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4 votes
2 answers
137 views

How to subtract a list from certain sublists of a list? [closed]

I have a problem in doing an operation on this vector {{2,3},{3,4},{5,6}}-{1,1} I want to minus this to get the result ...
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0 votes
1 answer
110 views

Second order differential operator in Mathematica

I am trying to write the code for the following expression in Mathematica: $$\partial_{x} e^{-g x}=-g e^{-g x}+e^{-g x} \partial_{x}\,.$$ I was able to do so with the help of the following links with ...
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  • 3
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0 answers
47 views

How to write the expression for first order differential operator in Mathematica?

How to write the expression for first order differential operator in Mathematica? What I mean to say that I want to evaluate $$\frac{\partial}{\partial x}f(x)=f'(x)+f(x)\frac{\partial}{\partial x}.$$ ...
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3 votes
1 answer
77 views

Define an operator for long equations

I'm trying to workout a long expression with derivations, the thing is I can't seem to transfer this problem to code. What I need is a operator $D = l^\mu \frac{\partial}{\partial x^\mu} $ where $l^\...
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  • 305
7 votes
1 answer
442 views

What operator is this?

I was looking at some sample code in a YouTube video and saw an "operator" (not sure this is the right term) consisting of a horizontal bar with circles on the ends. I searched through the ...
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0 votes
2 answers
64 views

How to define specify parameter functions of a Sturm-Liouville operator & plot its effect on specific functions?

I have a Sturm-Liouville operator: $$\mathcal{Ly(x)}=-\frac{\mathrm{d}}{\mathrm{d}x}\left(p(x)\frac{\mathrm{d}}{\mathrm{d}x}y(x)\right)-q(x)y(x)$$ but I do not yet know the parameter functions $p(x)$ ...
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  • 137
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Is there a concise way to generate a continuous less-than relationship?

Actually, I have a ton of variables, Let me simplify it to 4 in this post. vars = {a, b, c, d}; 0 < Less @@ vars < 10 0 < (a < b < c < d) < ...
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1 answer
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How can I remove the attributes "Orderless" from function Times stably and reliably?

Recently I have been doing some algebra of partitioned matrices, where product like below is common: where $A_{11}, A_{12}, X, Y$ are all partitioned matrix blocks thus all are matrices in essence. ...
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  • 383
3 votes
1 answer
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A possible issue in combination of the Infix operator ~ with Sequence [closed]

There are other similar questions on this site about using the Infix operator for more than two arguments, which I have read. But there is one thing that I wasn't able to understand and couldn't ...
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1 vote
0 answers
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Use self-defined operator symbol simplify formula

Mathematica is very useful and powerful in symbol compute, but some output isn’t concise if we didn’t simplify. Can i predefined some operator? eg. Lie bracket. Here is a minimum example. Suppose ...
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  • 445
0 votes
1 answer
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Defining Numerical Integral Functional [closed]

In some sense the question is a combination of defining an operator and defining numerical integration with parameters. For example, I want to define $I[f] = \int_0^1 f(x)dx$. and tried ...
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  • 101
1 vote
2 answers
51 views

System of rules transformingn a multivariate polynomial onto corresponding partial derivative operator

I take a complex multivariate polynomial, and I want to transform it into the corresponding differential operator. I.e., I am looking for the set of rules transforming variables to derivation, ...
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1 vote
1 answer
230 views

Simplifying quantum operators (ladder operators with multiple modes)

Similar to this question, I am interested in working with an implementation of quantum ladder operators. I've been trying to use this "Quantum Mathematica Package" to solve some lengthy ...
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3 votes
0 answers
120 views

Commutator of QFT Operators $[\hat{a}_p, \hat{a}^\dagger_k]$ and 4-Momentum Integrals

I just recently started looking into CAS (i.e. i have very little experience in Mathematica), specifically for doing basic calculations in Quantum Field Theory. For that i would like to define $\hat{a}...
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0 votes
2 answers
59 views

How to create an operator which is a composition of a sequence of operators?

Suppose I have a sequence of operators $\partial_x$, $\partial_x^2$,..., $\partial_x^n$. I want to define an operator which is a composition of these $D_x^{(n)}=\partial_x\circ\partial_x^2\circ\cdot\...
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7 votes
1 answer
135 views

Applying Operators inside complex expressions to argument with Through

I am developing some functions to help me work with Quantum Mechanics Momentum Operators. Here, for simplicity, I represent them with these simple functions because the actions of the operators ...
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  • 83
1 vote
2 answers
135 views

How to make a change of variable $y=x^2$ in the differential operator $\frac{d^2}{d y^2}$?

I have this differential operator $$\frac{d^2}{d y^2}\qquad (1)$$ I want to make a change of variable $y=x^2$ in $(1)$ so that I get this differential operator $$ \frac{1}{4 x^2} \frac{d^2 }{d x^...
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  • 335
0 votes
1 answer
52 views

Evaluating a scalar product of a vector and a differential operator vector

I created a scalar product of a vector $\in \mathbb{R}^2$ and of a vector consisting of a differential operators ...
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2 votes
4 answers
218 views

Coordinate transformation can this be done with AffineTransform?

Looking for alternatives or improvements for accomplishing the following: Given the position of points A, B, and C in both the x-y and u-v planes, determine transformation functions to map values ...
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1 vote
0 answers
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Performing operator expression on a function

What I want. I write an operator expression, and Mathematica performs it on a function. Examples: E^(b D): f[x] -> f[x+b] ...
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  • 2,751
2 votes
1 answer
183 views

Dealing with infinite matrices in Mathematica?

Is there a mechanism of dealing with infinite matrices in Mathematica, and in particular, with linear operators, corresponding to those matrices? For instance, automatic simplification of operator ...
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  • 2,751
1 vote
0 answers
76 views

Whole 2 line code, producing a bug (infix operator)

Copy the following code, and create new 0 byte file, and paste the code and save it to TEST.nb ...
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1 vote
1 answer
22 views

Generating composed operators using Table

Given an operator with two argumentsf[#1,#2]& and some positive (evaluated) integer n, I want to generate the operator ...
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  • 113
1 vote
0 answers
65 views

Composition of functions and operator forms of built-in functions

I am trying to replicate the behaviour of some of the built-in operator forms (for Map, Apply etc) but struggling to understand ...
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  • 362
1 vote
0 answers
40 views

Differential operator in Mathematica

I am fairly new to Mathematica and I wanted to know if I can define the following operator $E:=(x^2\sqrt{1-K(x^2+y^2+z^2}+y^2+z^2)\gamma^{1}\partial_{1}+(y^2\sqrt{1-K(x^2+y^2+z^2}+x^2+z^2)\gamma^{2}\...
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0 votes
0 answers
86 views

How to implement this operator in Mathematica?

I am interested to implement this operator: $$(\ln D)[f] =\left(\frac{i \pi}{2}-\gamma\right) f(x)+\frac{1}{2}\,\text{P.V.}\int_{-\infty}^\infty \left(\frac{1}{x-x'}-\frac{1}{| x-x'| }\right)\,f(x')\,...
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  • 2,751
0 votes
0 answers
61 views

Can I apply functions to infinite matrices or linear operators in Mathematica?

I do not know how can I apply functions to infinite matrices or linear operators. For instance, having the derivative operator, what is its sine? For instance, for finite derivative operator we have $$...
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  • 2,751
4 votes
1 answer
219 views

How can I direct sum matrices into the middle of one another another?

I would like to execute the mathematical operation of the direct sum of matrices in the case where the matrices are not appended one after the other along the diagonal, but instead mixed among one ...
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  • 43
0 votes
3 answers
81 views

Take function as input for other function, access variable

I am very new to Mathematica, and I searched the documentation and google now for quite some time. Let's say, I want to implement a mathematica function, that does the following mapping: $f(t)\mapsto \...
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3 votes
0 answers
69 views

Mathematica Refuses to Output ContourIntegral and DoubleContourIntegral in Nice Mathematical Notation

I experience a strange behaviour of handling the Contour and Double Contour Integral symbols \[ContourIntegral] and \[DoubleContourIntegral] in Mathematica. Whatever I try theyy behave differently ...
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  • 2,751
0 votes
0 answers
30 views

Simplifications and error in matrix integral operator

I defined the matrix integral operator ...
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1 vote
1 answer
37 views

DIsplaying the product of matrix operations

I am struggling to find out the option that show the final result of a matrix operations and not the necessary steps to achieve the result. The last line of the following picture demonstrates the ...
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0 votes
1 answer
35 views

How to apply a function if an expression evaluates to true

I'm trying to define a simple function that will accept a symbol and an expression, set the symbol equal to the expression, and then print out info about the equation. Like so: ...
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0 votes
1 answer
106 views

commutator between tensor products

I am interested in some quantum mechanical calculations in Mathematica. I am working with a tensor product of Hilbert spaces $\mathcal H = \mathcal H_1\otimes \mathcal H_2$. I would like to implement ...
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  • 133
1 vote
1 answer
135 views

Quantum Mechanics operators

$$\sigma_{z}^{A}|\downarrow\rangle_{A}=-|\downarrow\rangle_{A}$$ $$\sigma_{z}^{A}|\uparrow\rangle_{A}=|\uparrow\rangle_{A}$$ We have the above relations in Quantum mechanics. Is there a way to ...
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3 votes
1 answer
111 views

execute a summation involving a differential operator

Below is an operator $\hat{D}=\sum_{i,j}^2 \frac{\partial}{\partial u^i}\sqrt{g}g^{ij}\frac{\partial}{\partial u^j}$ where $g_{ij}=\begin{pmatrix}p(x,y) & q(x,y)\\\ q(x,y) & r(x,y)\end{pmatrix}...
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  • 153
3 votes
2 answers
704 views

Generating a random density matrix in Mathematica

I am interested in using Mathematica to generate random $N\times N$ density matrices describing pure quantum states; for the less physics-oriented folks, a density matrix is positive semi-definite, ...
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0 votes
0 answers
76 views

Defining an mathematical operator

I'm trying to learn mathematica to use in my thesis. I have basic problems with definitions, calculations etc. Let me ask a question. I want to define anti derivative operator and derivative operator, ...
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6 votes
3 answers
454 views

Iterated differential operator

I would like to implement the following differential operator in Mathematica, $$ \prod_{j=1}^n \left({\mathrm d \over \mathrm d x}-j\right) $$ On a case by case basis, I can just expand it out and ...
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2 votes
0 answers
59 views

Precedence of @@ vs /@ [closed]

How do I find what I think is called the "precedence" of a given operator. That is, for the following code: ...
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  • 101
3 votes
2 answers
63 views

Define the behavior of operators without built-in meaning

I need an operation $\tilde{}$ that lifts another operation (for example, the sum, but this does not have to be limited to real numbers) in the sense that $\widetilde{ (x \oplus y)} = \tilde x + \...
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  • 155
2 votes
0 answers
57 views

Define an operator with the distributive property that works in general expressions

This is a follow up to this question. In that question they use TagSetDelayed to give a symbol the distributive property. In my case this becomes ...
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4 votes
1 answer
467 views

Partial transpose of 8x8 density matrix?

Please could someone help me to knew how to compute the partial partial-transposition of the following matrix? mat = Table[ρ[i, j], {i, 1, 8}, {j, 1, 8}]
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  • 629
0 votes
1 answer
58 views

How to define derivative operation of a series acting on normal function

In some cases, I have to do derivarive of higher order acting on some function successively. Here is a toy example: I have a function named myfunc: ...
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  • 1,123
2 votes
1 answer
53 views

Is associativity of operators documented?

Operator precedence is documented. Operators without built-in meanings are documented. The word "associative" apparently does not appear in either page. It's easy enough to do an experiment to observe ...
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