Questions tagged [operators]
Questions about using or composing operators--functional mappings from one state or vector space to another.
16
votes
3answers
642 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
298 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
58 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
45 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
59 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
46 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
71 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
73 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
98 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
61 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
104 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
54 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
139 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
...
1
vote
0answers
45 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
0answers
82 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
77 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
66 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
477 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:
...
7
votes
1answer
158 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
36 views
Non-commutative multiplication sign and constant treatment
By default, non-commutative multiplication behaves as
(-W) ** (4 R) //FullForm
...
1
vote
1answer
49 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
54 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
147 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
169 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
54 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
61 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
120 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
63 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
$$X = \sum_{j=-\infty}^n ...
5
votes
2answers
129 views
How to construct infix operator with usual behavior?
I am trying to define my own infix operator and having problems with strung-together evaluation. The code below is a simple example. What I would like is to have the operator treated associatively, ...
2
votes
1answer
301 views
What are current approaches for supporting Dirac notation for quantum mechanics?
I'd like to be able to use Mathematica to preform some basic quantum mechanics and quantum computation operations using Dirac's Bra-Ket notation.
I've seen several solutions to defining basic ...
3
votes
1answer
436 views
4
votes
2answers
290 views
Interchanging addition and multiplication
Suppose I have an expression that employs addition and multiplication, but no subtraction or division:
$$
2 a + 5 b x^3 + c \;.
$$
I would like to change this to
$$
(2 + a) (5 +b + x +x +x) c \;,
$$
...
1
vote
0answers
47 views
Operator on a multivariable function in a sum
I need to define an operator that does as follow for any function $h_m$.
$\qquad O[h_m](k,M,b,l_{max})=\sum_{l\neq (0,m)}^{l_{max}}il \left (h_l(k,M,b,l_{max}) b_{m-l}(k)- c_l\partial_k h_{m-l}(k,M,...
1
vote
2answers
102 views
Defining an operator: Partially evaluate a Pure Function
I would like to define an operator that takes some parameters as input and returns a function. Here is an example:
...
3
votes
2answers
932 views
Matrix differential operator
i'm new in MATHEMATICA. I want to create an operator $D^{(f)}=\partial_x+f'-\partial^2_x$ and $D^{(g)}=\partial_x+g'-\partial^2_x$ and put it into a matrix element, then multiplied by a vector whose ...
4
votes
2answers
105 views
Define an operator for FileNameJoin
When I join file names, it's inconvenient to use FileNameJoin. The workaround is to use <> instead, however <> is not exactly like FileNameJoin.
I tried to define an operator . It just doesn't ...
0
votes
1answer
105 views
How to efficiently exponentiate a differential operator with non-commuting terms, acting on an infinite series?
My question is related to
this one, but I am more explicit with the form of the operator in the exponential and the function $f$.
Let us have the expression:
$$ e^{\mathrm{i} \left( f(x)(\hat{q} \...
3
votes
1answer
99 views
Single argument operator form?
I've heard the explanation that functions like StringDrop[] are varargs and so that is why they do not have an operator form.
But when you are only using the ...
-1
votes
1answer
63 views
3
votes
2answers
153 views
A function which maps $(ax + by)(cx + dy) \mapsto (a \partial_x + b \partial_y) (c \partial_x + d \partial_y)$
I am new to Mathematica and, as the title says, looking for a way of mapping (for example) the polynomial $$(ax + by)(cx + dy) \mapsto \left(a \frac{\partial}{\partial x} + b \frac{\partial}{\partial ...
0
votes
1answer
48 views
Symbollic integration and differentiation of operated functions
This question is a continuation of this one.
I used the answer provided in the previous question to write this code
...
13
votes
2answers
435 views
How I can define this operator in Mathematica?
I want to define an operator $G$ such that
$$G(f):=\begin{cases}f(\{x\}),&\lfloor x\rfloor\text{ is even}\\\frac1{f(\{x\})},&\lfloor x\rfloor\text{ is odd}\end{cases}$$
for any function $f$, ...
2
votes
0answers
54 views
Defining the Distributive Depth of an Operator
I am working on defining the relations between Bras and Kets in Mathematica, and I am using the CircleDot operator to represent multiplication. I seem to have some trouble defining how operations on ...
11
votes
2answers
290 views
What is the best way to define Wirtinger derivatives
Wirtinger derivatives ( also called Cauchy operators) in complex analysis are widely used tools. They are defined in the case of one dimensional complex plane as follows
$$\frac{\partial}{\partial z}=...
