Questions tagged [operators]
Questions about using or composing operators--functional mappings from one state or vector space to another.
0
votes
1answer
79 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
90 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
55 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
130 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
37 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
43 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
58 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
35 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
88 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
46 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
82 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
34 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
$$ \Delta_i (\sum_{n=0}^\infty c_n x_i^n) = \sum_{n=1}^\infty c_n x_i^{n-1}, \quad \Delta_i ...
20
votes
3answers
744 views
What is the definition of Curl in Mathematica?
I have a usual mathematical background in vector and tensor calculus. I was trying to use the differential operators of Mathematica, namely Grad, ...
2
votes
2answers
300 views
=== not working properly [closed]
I've been trying to check the identity using wolfram Mathematica and I've found the following
...
0
votes
1answer
63 views
Reduction of differential operators
Suppose my code outputs the expression
$$\frac{f^{(0,2)}(r,\phi )+r \left(f^{(1,0)}(r,\phi )+r f^{(2,0)}(r,\phi )\right)}{r^2}$$
This is simply the Laplacian $\nabla^2f(r, \phi)$. Is there a way ...
0
votes
0answers
67 views
Commutator of differential operators
Let $P_x = \frac{\hbar}{i}\frac{d}{dx}$, after specifying the commutator relation symbolically $[X, P_x] = i\hbar$, I can ask Mathematica to calculate commutator algebra. My question: is there a way ...
0
votes
1answer
68 views
Divergence and gradient operators in two dimensions
Divergence of a vector $\mathbf{a}$ can be numerically written as,
\begin{eqnarray}
\nabla \cdot \mathbf{a} \approx \sum_{i=0-9} w_i\mathbf{a(x+c_i)}\cdot \mathbf{c}_i
\end{eqnarray}
The lattice ...
0
votes
2answers
50 views
Sum over integer partition with variable function argument
Define
$$\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
74 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 ...
1
vote
1answer
97 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?
...
3
votes
4answers
104 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
65 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
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 ...
2
votes
3answers
116 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
59 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
140 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
85 views
Distribute operator
I have an operator defined by \[ScriptCapitalN] and want to Expand a term and then use ...
1
vote
0answers
49 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
94 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 ...
2
votes
1answer
110 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
84 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
33 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
39 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
61 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
70 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 ...
4
votes
2answers
508 views
How to define a differential operator in Mathematica? [duplicate]
I want to define an operator $(\partial_{t}+1)^{2}=\partial_{t}\partial_{t}+2\partial_{t}+1$. Then, I want it to act on $t$. My code looks like this:
...
8
votes
1answer
163 views
Position-based Inline syntax for Curry
I would like to update an existing pseudo-curry function:
• /: h_[pre___, •, post___] :=
Function[expr, h[pre, expr, post]];
that I use inline like this - the ...
0
votes
0answers
42 views
Non-commutative multiplication sign and constant treatment
By default, non-commutative multiplication behaves as
(-W) ** (4 R) //FullForm
...
1
vote
1answer
50 views
Finding a pattern in sum of products of two or more variables with subscripts
I am trying (so far unsuccessfully) to isolate terms in an expression which are product of variables with a specific subscript pattern (the b_,_'s). I want only terms for which the first subscript ...
0
votes
0answers
62 views
How to use multiple placeholders to define a function that operates on special functions.
I am trying to understand if and how I can use multiple placeholders in order to define a function that will perform more than one operations on special functions; more accurately, sums, products, etc ...
2
votes
1answer
158 views
Linear operator algebra: How to distinguish scalars and operators?
In the book "A Physicist' s Guide to Mathematica" Patrick Tam introduces symbolic rules for an algebra of linear operators. Mathematically the rules are as follows, where upper (lower) case letters ...
0
votes
3answers
180 views
Calculating bracket operations [closed]
Is there a way to calculate commutation relations in Mathematica? For example, let's say I want to compute ; how can this be done?
0
votes
0answers
55 views
How to create operator variables and lists of operators?
I want to know if it is possible to create a variable that is an operator. (Please note I only started programming Mathematica today) For example, the partial operator $\partial_x$ i.e.
...
4
votes
1answer
69 views
1
vote
0answers
65 views
Superposition of the differential operators
My problem can be easily solved without Mathematica, however, I am curious how to do it in Mathematica. Moreover, I can be stuck with a similar, but more cumbersome problems in the future.
Following ...
1
vote
1answer
136 views
Raising, lowering and number operators for Dirac notation
Starting from this very interesting post Defining quantum-mechanical Bra and Ket operations, i would like to implement raising, lowering and number operators, taking into account that they might be ...
0
votes
0answers
71 views
How to define a product on formal power series (pseudo-differential operators)?
I am used to working with the set of (algebraic) pseudo-differential operators, which consists of formal power series in the symbol $D$ (differentiation operator) of the form
$$X = \sum_{j=-\infty}^n ...
5
votes
2answers
135 views
How to construct infix operator with usual behavior?
I am trying to define my own infix operator and having problems with strung-together evaluation. The code below is a simple example. What I would like is to have the operator treated associatively, ...
2
votes
1answer
349 views
What are current approaches for supporting Dirac notation for quantum mechanics?
I'd like to be able to use Mathematica to preform some basic quantum mechanics and quantum computation operations using Dirac's Bra-Ket notation.
I've seen several solutions to defining basic ...
3
votes
1answer
443 views
