Questions tagged [operators]

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

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2answers
55 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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50 views

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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1answer
61 views

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. ...
3
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1answer
82 views

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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0answers
79 views

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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1answer
37 views

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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2answers
48 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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1answer
149 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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0answers
87 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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2answers
54 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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1answer
129 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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2answers
127 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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1answer
47 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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4answers
178 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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Quantum mechanical broadband operators

Is there a way to define broadband operators as used for example in quantum optics in Mathematica? As an example, if $\hat{a}_k$ denotes a regular second quantization operator for some plane wave ...
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0answers
43 views

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] ...
2
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1answer
167 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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0answers
74 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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1answer
21 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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0answers
58 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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0answers
36 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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0answers
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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0answers
60 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 $$...
4
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1answer
196 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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3answers
73 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 \...
3
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0answers
62 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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0answers
29 views

Simplifications and error in matrix integral operator

I defined the matrix integral operator ...
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1answer
36 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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1answer
34 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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1answer
87 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 ...
1
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1answer
103 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 ...
3
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1answer
100 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}...
3
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2answers
559 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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0answers
73 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, ...
6
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3answers
438 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 ...
2
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0answers
56 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: ...
3
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2answers
59 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 + \...
2
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0answers
45 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 ...
4
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1answer
286 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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1answer
52 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: ...
2
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1answer
50 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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0answers
70 views

Evaluating a differential expression using Mathematica

I am attempting to calculate the following expression in Mathematica, but I am having a bit of difficulty doing so. I want to calculate the following expression \begin{gather*} \left(x^2\sqrt{1-...
3
votes
2answers
79 views

How to check if all the members of a list lies in specific ranges based on another list?

There are two lists as follows: lista = {i, j, k}; listb = {{1, 2}, {3, 4}, {5, 6}}; If i in ...
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0answers
41 views

Create an operator that holds its arguments [duplicate]

How can I create an operator that holds its arguments? I am looking to define something similar to oper[x_][expr_] := Hold[expr] I am expecting the following ...
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3answers
653 views

How to calculate the divergence of stress matrix in polar coordinate system correctly

I calculate the divergence of stress matrix in polar coordinate system by the method of coordinate transformation as follows : ...
7
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2answers
453 views

Defining an operator in Mathematica?

How to define the following operator in Mathematica? $$\hat{\nabla}^4=\left(\frac{\partial^2}{\partial\hat{r}^2}+\frac1{\hat{r}}\frac{\partial}{\partial\hat{r}}\right)^2$$
3
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1answer
74 views

How to expand (not replace) the "+", ">" infix operator on strings? [duplicate]

I went through the similar questions to overload the behavior of built-in operator, like How to overload the operator "*" as KroneckerProduct. The answers given there are usually to use new ...
19
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1answer
205 views

Why does OperatorApplied by default reverse the arguments?

Perhaps this is just one of those Mathematica curiosities, but I'd like to know why by default OperatorApplied[f][x][y] === f[y,x] versus the more usual way one ...
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0answers
72 views

Nest function n times

A trivial example would be f[x_]:=x Nest[f, 7, n] which would of course be 7 because it is independent of ...
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3answers
121 views

How to use `Through` function to pass through derivative operator

Because of the need of the operation rules of variational notation, I want to achieve the following effects: Through[(f + s)'[x]] Through[(f + s)''[x]] I want to ...

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