Questions tagged [operators]
Questions about using or composing operators--functional mappings from one state or vector space to another.
191
questions
0
votes
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 ...
1
vote
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 ...
2
votes
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}...
4
votes
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 ...
0
votes
0answers
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)...
0
votes
0answers
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) \...
0
votes
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 ...
0
votes
0answers
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\...
0
votes
0answers
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 ...
0
votes
0answers
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} + \...
0
votes
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):
...
10
votes
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 <...
3
votes
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 ...
0
votes
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]
<...
0
votes
0answers
37 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 ...
0
votes
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:
...
3
votes
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 ...
1
vote
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
2
votes
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 ...
0
votes
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 ...
2
votes
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 ...
1
vote
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
...
2
votes
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
votes
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 ...
1
vote
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
vote
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]]]+....,$$
where $[A,B]=AB-BA$. In the case of my problem, $[B,...
2
votes
2answers
45 views
Defining a differential operator that acts on a non-commutative basis
Given a non-commutative basis ${x_0,x_1,x_2}$ I'd like to define a differential operator that acts as so
$$ \Delta_i (\sum_{n=0}^\infty c_n x_i^n) = \sum_{n=1}^\infty c_n x_i^{n-1}, \quad \Delta_i ...
20
votes
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
votes
2answers
324 views
=== not working properly [closed]
I've been trying to check the identity using wolfram Mathematica and I've found the following
...
1
vote
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 ...
0
votes
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 ...
0
votes
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 ...
0
votes
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 = ...
0
votes
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 ...
0
votes
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
votes
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(...
0
votes
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:
...
1
vote
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
votes
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
votes
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
votes
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
votes
1answer
107 views
Distribute operator
I have an operator defined by \[ScriptCapitalN] and want to Expand a term and then use ...
1
vote
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
votes
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
votes
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
votes
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 ...
1
vote
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}, \...
0
votes
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. ...
0
votes
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 \...
0
votes
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 ...
