Questions tagged [operators]
Questions about using or composing operators--functional mappings from one state or vector space to another.
236
questions
0
votes
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 $p(x)$ ...
0
votes
0answers
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) < ...
0
votes
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
votes
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 ...
1
vote
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 ...
0
votes
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
...
1
vote
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, ...
0
votes
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 ...
3
votes
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}...
0
votes
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\...
7
votes
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 ...
1
vote
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^...
0
votes
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
...
2
votes
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 ...
0
votes
0answers
42 views
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 ...
1
vote
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
votes
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 ...
1
vote
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
...
1
vote
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 ...
1
vote
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 ...
1
vote
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}\...
0
votes
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')\,...
0
votes
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
votes
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 ...
0
votes
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
votes
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 ...
0
votes
0answers
29 views
1
vote
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 ...
0
votes
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:
...
0
votes
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
vote
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
votes
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
votes
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, ...
0
votes
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
votes
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
votes
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
votes
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
votes
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
votes
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}]
0
votes
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
votes
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 ...
0
votes
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 ...
1
vote
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 ...
-5
votes
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 :
...
asked Mar 30 '20 at 5:06
A little mouse on the pampas
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7
votes
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
votes
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
votes
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 ...
0
votes
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 ...
0
votes
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 ...
asked Feb 21 '20 at 6:50
A little mouse on the pampas
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