Questions tagged [operators]

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

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0answers
29 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
107 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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2answers
62 views

How can I concisely define a matrix-form partial derivative operator?

I have a vector $\boldsymbol{u}(x,y) = \begin{bmatrix} u_x(x,y) \\ u_y(x,y) \\ \end{bmatrix}.$ I would like to get $\boldsymbol{\sigma}(x,y) = \begin{bmatrix} \sigma_x \\ \sigma_y \\ \tau_{xy}...
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2answers
190 views

Can C-like function call syntax be easily achieved for particular function names?

I'm trying to use Mathematica as a tool to prove that some C code is equivalent to another (up to roundoff errors). For this I need to somehow paste C expressions like ...
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62 views

Simplifying a differential equation acting on a product of functions

I have a function $f(x_1, \ldots , x_n)$ in $n$-variables that satisfies a fourth order linear differential equation (say $Df=0$). The function $f(x_1, \ldots, x_n)$ is of the form $f(x_1, \ldots, x_n)...
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45 views

Using FullSimplify to simply expressions involving differential operators

I am trying to simplify some long formulas involving differential operators in $n$ variables. For example, I want to simplify $$\left(\frac{\partial}{\partial x}-\frac{\partial}{\partial y}\right) \...
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1answer
76 views

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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27 views

How to transform polynomial to differential operator?

How to transform the multiariate polynomial to corresponding differential operator? For instance, for a polynomial $ \frac{1}{2} z_1^2 z_3^6 $ is the goal operator $ \frac{\partial ^8}{\partial ^2x_1\...
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33 views

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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46 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
75 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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4answers
370 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
92 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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1answer
64 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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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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2answers
165 views

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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2answers
136 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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4answers
143 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
44 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
63 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
86 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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1answer
40 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 ...
2
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1answer
113 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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1answer
67 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 ...
1
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1answer
88 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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2answers
45 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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4answers
899 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, ...
2
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2answers
324 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
86 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
197 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
82 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
81 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
79 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
213 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
144 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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2answers
76 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: ...
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0answers
22 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 ...
2
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3answers
143 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 ...
4
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1answer
67 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: ...
5
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1answer
146 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 ...
2
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1answer
107 views

Distribute operator

I have an operator defined by \[ScriptCapitalN] and want to Expand a term and then use ...
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0answers
53 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 ...
5
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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 ...
4
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2answers
231 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: ...
2
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1answer
125 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 ...
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0answers
38 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
43 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
64 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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1answer
94 views

How to program Mathematica to do the differential operator calculation

I want to create a surface Laplacian under the spheroidal coordinates, Now, I already have the surface gradient defined, but I don't know how to find the Laplacian. Since the surface gradient is too ...