# Questions tagged [operators]

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

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### Simplifications and error in matrix integral operator

I defined the matrix integral operator ...
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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### Defining and Squaring an Operator using Mathematica

Hello I have a question regarding the possibility of defining a operator using Mathematica. Essentially what I would like to do is define the following, \begin{gather*} {\mathcal D := \frac{1}{(x^2+...
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### 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-...
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### 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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### 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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### 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 : ...
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### Defining an operator in Mathematica?

How to define the following operator in Mathematica? $$\hat{\nabla}^4=\left(\frac{\partial^2}{\partial\hat{r}^2}+\frac1{\hat{r}}\frac{\partial}{\partial\hat{r}}\right)^2$$
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### 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 ...
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### 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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### Problem with makeOperator which yields Polynomials of an operator

Hi Is it possible to improve the macro provided by Jens Polynomial expansion of operator ...
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### 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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### 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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### Simplifying $\left(f\left(x\right)\frac{\partial}{\partial x}\right)^nf\left(x\right)$ into a summation

In case you're wondering how to get differentials to act like operators in Mathematica, I stumbled across a package Carl Woll made to solve this issue in this question. There's a a more recent version ...
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### Implicit definition of a coordinate in differential equation [duplicate]

I would like to solve the following differential equation $\frac{d^2 \psi(r_*)}{dr^2_*} + (\omega^2 - V(r)) \psi(r_*)=0$ and the boundary conditions are $\psi(\inf) = \psi(-inf) = 0$. The problem is ...
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### Multiply function-valued matrices

I would like to create a notebook for calculations in supersymmetric quantum mechanics. The basic building blocks are two functions (or maybe better: operators): ...
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### Operator currying: how to convert f[a,b][c,d] to {a+c,b+d}?

This question is related to this golfing question (but I'm not interested in golfing, only in functional operator composition): How can we convert f[a,b][c,d] to <...
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### Best way to apply a list of functions to a list of values?

This question is closely related to questions 83720, 17460, and 11298. How would you write the operator F = Through[#1[#2]] & in the prettiest, fastest, or ...
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### How to substitute integral operators into polynomials?

Suppose I have a polynomial $a_0+a_1 f(x,t) + a_2 f(x,t)^2 + ....$. In code, a0 + a1 y + a2 y^2 + a3 y^3 /. y :> Integrate[Subscript[y, k] E^(I k y), k] <...
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### Defining a function through an ODE containing unspecified operators

I want to do some algebra using a function only defined through a DE containing unspecified operators. The DE is $$\partial_zu(z) = \left[\hat{D}+\hat{N}(z,u)\right] u(z).$$ Here $u$ lives in ...
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### How to construct — based on physics-type notation — a magical simplex $\mathcal{W}$ of bipartite qutrits?

I have a short Mathematica program: ...
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### Append a function of an expression as operator form using Curry?

I fielded this q to tech support but didn't get a conclusive answer yet: Is it possible to use Curry specifically to modify ...
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### Distribute && over a list [duplicate]

I cannot find an operator "RO" so that given a list, say {a,b,c}, RO[&&,{a,b,c}] produces a && b && c
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### Skipping indices in a product

I have a matrix $A$ for which I want to compute the quantity $T\lambda_j = \Pi_{\lambda_i\ne \lambda_j} \frac{A - \lambda_i I}{\lambda_j-\lambda_i}$, where $\lambda_i$ ($\lambda_j$) denote the ...
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I have a map defined as $\qquad \Phi(X) = a^2\, Tr[X] |0\rangle \langle 0| + b^2\, Tr[X] |1\rangle \langle 1| + a\,b\, Tr[\sigma_z X] |0\rangle \langle 1| + a\,b\, Tr[\sigma_z X] |1\rangle \langle ... 1answer 148 views ### Problem with defining a simple linear operator I need to define a linear operator, which should have very simple linearity: myOp[Plus[f_, g_]] := myOp[f] + myOp[g] myOp[a_ f_[x_, t_]] := a myOp[f[x, t]] where ... 2answers 124 views ### Simplify differential expressions One can differentiate a two dimensional vector like this, ClearAll["Global`*"] u[x_, y_] := {f[x, y], g[x, y]} Div[u[x, y], {x, y}] with output ... 1answer 41 views ### Define different actions for the same operator depending on the nature of its arguments I am working with terms of the form A**B1**B2 where A, B1, and ... 1answer 140 views ### Defining an operator with given properties In symbolic derivations with Mathematica, one often needs to define an operator with some desired properties, which will be used to stand for a general function or transform. For example, I would ... 1answer 89 views ### Define custom operator and specific application I want to define a specific operator that will act in generic functions that depend, say, in the variable z. My problem is that I want when a specific function is ... 1answer 93 views ### A program for finding the summation of an analytical expression Consider the Baker-Hausdorff formula for two operators$A$and$B$: $$e^BA e^{-B} =A+[B,A]+\frac{1}{2!}[B,[B,A]]+\frac{1}{3!}[B,[B,[B,A]]]+....,$$ where$[A,B]=AB-BA$. In the case of my problem,$[B,...
Given a non-commutative basis ${x_0,x_1,x_2}$ I'd like to define a differential operator that acts as so  \Delta_i (\sum_{n=0}^\infty c_n x_i^n) = \sum_{n=1}^\infty c_n x_i^{n-1}, \quad \Delta_i ...