Questions tagged [operators]

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

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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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34 views

How to compute gauge variation of expression?

Suppose I have a symmetric tensor field $h_{\mu\nu}$ I want to implement somehow the following gauge variation of this tensor field as follows $\delta h_{\mu\nu} = \nabla_{\mu}\epsilon_{\nu} + \...
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1answer
57 views

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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1answer
263 views

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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1answer
75 views

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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4answers
851 views

What is the definition of Curl in Mathematica?

I have a usual mathematical background in vector and tensor calculus. I was trying to use the differential operators of Mathematica, namely Grad, ...
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1answer
57 views

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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36 views

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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1answer
149 views

Wick's theorem for Gaussian stochastic variables

I wonder whether there exists a clever way to implement Wick's theorem for Gaussian stochastic variables $\eta_{j_{i}}$ (with $\langle \eta_{j_{i}}\rangle=0$ for $\forall i$) which in general states: ...
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2answers
103 views

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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0answers
56 views

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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1answer
93 views

Distribute operator

I have an operator defined by \[ScriptCapitalN] and want to Expand a term and then use ...
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4answers
135 views

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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1answer
41 views

Performing a simple operation with operators [closed]

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 ...
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1answer
45 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 ...
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2answers
70 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 ...
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2answers
130 views

How can I define operators that implement the algebra of sets?

I need to define some operators with properties like idempotence and distribution over union and intersection so that Mathematica can symbolically simplify expressions. How do I define such operators? ...
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1answer
37 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 ...
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1answer
96 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 ...
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0answers
165 views

Defining a complex partial differential operator

I tried to define a partial differential operator using this code ...
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2answers
39 views

Defining a differential operator that acts on a non-commutative basis

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 ...
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1answer
52 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 ...
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1answer
83 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,...
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4answers
218 views

How to implement the action of a shift operator on arbitrary functions?

How can I expand expressions like $$(1-g(x)D)\frac{1}{1-f(x)D},$$ where $f(x),g(x)$ are some functions and $D$ is the shift operator defined by $Dh(x)=h(x+a)D$. What I'm trying to do is to formally ...
2
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2answers
304 views

=== not working properly [closed]

I've been trying to check the identity using wolfram Mathematica and I've found the following ...
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1answer
70 views

Reduction of differential operators

Suppose my code outputs the expression $$\frac{f^{(0,2)}(r,\phi )+r \left(f^{(1,0)}(r,\phi )+r f^{(2,0)}(r,\phi )\right)}{r^2}$$ This is simply the Laplacian $\nabla^2f(r, \phi)$. Is there a way ...
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0answers
106 views

Commutator of differential operators

Let $P_x = \frac{\hbar}{i}\frac{d}{dx}$, after specifying the commutator relation symbolically $[X, P_x] = i\hbar$, I can ask Mathematica to calculate commutator algebra. My question: is there a way ...
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1answer
71 views

Divergence and gradient operators in two dimensions

Divergence of a vector $\mathbf{a}$ can be numerically written as, \begin{eqnarray} \nabla \cdot \mathbf{a} \approx \sum_{i=0-9} w_i\mathbf{a(x+c_i)}\cdot \mathbf{c}_i \end{eqnarray} The lattice ...
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2answers
54 views

Sum over integer partition with variable function argument

Define $$\hat{X}(Y) = [X,Y] $$ I have known matrices $S_i$ and $V$. I am trying to use Mathematica to define a function which calculates $$ \sum_{\substack{n_1, \ldots, n_k>1\\ n_1+\ldots n_k = ...
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1answer
77 views

Lowering operator for spherical harmonics [duplicate]

I need to be able to generate all of the $ l=2 $ spherical harmonics using the lowering operator. The specific question is listed below. Any assistance would be much appreciated! Thanksenter image ...
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1answer
135 views

Partial trace and Partial Transposition of a matrix easily? [closed]

Could someone help me to understand as to how to compute the partial trace and partial-transposition of an arbitrary matrix? I mean, is there any code to carry out these operations in Mathematica? ...
2
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4answers
112 views

define an operator

How is it possible to define the operator $(x+\frac{d}{dx})^n$ as a function of $n$? I use op[x_] = (x + D[#, x]) &; with the action on, for example, $\cos(...
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3answers
123 views

Noncommutative Expand into power series

I am new to Mathematica and am trying to apply it to quantum mechanics problems. The practice project I am dealing with now is considering quantum harmonic oscillator and ladder operator algebra ...
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2answers
70 views

A list of operators in the For cycle

I'm pretty sure that analogous questions have been asked here a zillion of times, but... I think it is pretty straightforward from the code what I expect it to give: ...
5
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1answer
142 views

Associativity of upvalue

how can I ensure the following definition to be associative? Unprotect[Times]; a_ f[x_] + b_ f[y_] ^:= f[a x + b y] Protect[Times]; gives me ...
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0answers
20 views

Operator valued functions [duplicate]

For some parts of physics it is useful to define an operator valued function Take for example R[K_] := Sum[K[[j]] D[#, K[[j]]], {j, 1, 4}] It is supposed to be ...
4
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1answer
60 views

Operator form for Histogram of multiple datasets?

I would like to plot a histogram for multiple datasets in a dataset query, but can't quite seem to make it work in operator notation: ...
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0answers
50 views

Add operator symbols to matrices in Wolfram [closed]

I am working with the matrices of the form $u = \begin{pmatrix}Y &y\\0 & Y\end{pmatrix}$, and I have an operator $a$ such that $au=\begin{pmatrix}Y & ay\\0 & Y\end{pmatrix}$. Since y ...
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2answers
245 views

Which operators are missing from the official precedence table?

I often use the Operator Input Forms page as a reference for operator precedence as well as which (used or unused) operators exist. However, I just noticed that at least one operator is missing from ...
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1answer
95 views

Indefinite order of differential operator

In the latest version of Mathematica, D can compute derivatives of symbolic order, that is, the $n^{\text{th}}$ (partial) derivative, returning an expression ...
12
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6answers
1k views

Element-wise test on List elements

This question could sound pretty silly but I can't find a way to apply element -wise tests to a list. For example if I digit ...
4
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2answers
97 views

Changing the grouping of an user defined infix operator [duplicate]

How can I change the default grouping on an operator without a built-in meaning? I've created my own infix operator by defining LeftArrow. ...
8
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4answers
505 views

Change Operator Precedence of --> operator

I am trying to use --> operator with highest precedence ...
2
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1answer
90 views

Commutator of block matrices

How to implement a commutator of matrices composed of operators? Background: Let $\hat A_{ij}$, $\hat B_{kl}$ be some sets of some operators. $\hat I$ is the identity operator. Their commutators are ...
7
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3answers
2k views

Creating the Nabla operator (also known as Del operator) as an operator

How can I define the nabla operator (also known as Del operator) as a an operator, acting on everything to the right of the operator! Also taking \[Del]^2 would ...
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0answers
36 views

Del as a Differential Operator: (Matrix times Del) cross vector [duplicate]

I tried to reply to this answer, but don't have enough reputation points yet. Basically the poster constructed Del (i.e. $\nabla = \left( \frac{\partial}{\partial x}, \frac{\partial}{\partial y}, \...
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0answers
40 views

How do you treat gradient as a vector? [duplicate]

I need to express $\nabla = (\partial_x,\partial_y,\partial_z)$ as a vector, so that I can compute the differential operator given by $A\cdot\nabla$ (where here $A$ is a 3x3 matrix) using Mathematica. ...
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1answer
63 views

How can I define a derivation in Mathematica?

I would like to define a derivation in Mathematica. As an example something like this: for an operator O and operators $A,B$ in a two dimensional vector space with $$ O \times A = a \\ O \times B = b \...
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2answers
1k views

Defining the Moyal Product in Mathematica

What would be the best way to define the Moyal Product, $f(x,p)\star g(x,p)$, in Mathematica? $f(x,p)\star g(x,p)$ may be written as $f\star g=\sum\limits_{n=0}^{\infty}\frac{1}{n!}\left(\frac{i\hbar}...