Questions tagged [operators]

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

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62
votes
2answers
4k views

when is f@g not the same as f[g]?

I have always thought that f@g will give the same result as f[g] in all cases, and it is just a matter of style which one to use ...
30
votes
6answers
5k views

Having the derivative be an operator

How do I create an operator which acts like a derivative to everything to the right of it: for example: $ \left( \partial_x + \partial_y + z \right ) x \psi $ How do I make that evaluate to: $x \...
65
votes
6answers
3k views

V10's Operator Forms - what are they good for?

V10 introduces an operator form for several functions perhaps primarily due to their role in queries as part of introducing data science functionality. At first pass it seems a lot of effort to add ...
10
votes
3answers
4k views

Using D to find a symbolic derivative

I need to do the following: Define a function Take the derivative of this function and have a look at the symoblic representation Substitute in some values With the bonus that I want to use the ...
24
votes
3answers
2k views

How is + as an infix operator associated with Plus?

How is + associated with Plus? Suppose I want to define a head FooBar and have it ...
14
votes
3answers
659 views
5
votes
4answers
5k views

How to write a differential operator in Mathematica

I have a very basic question. I am trying to code the LHS of the differential equation: $$\Big[\frac{1}{\sin\theta}\frac{d}{d\theta}\big(\sin\theta\frac{d}{d\theta}\big)-\frac{m^2}{\sin^2\theta}+n(n+...
6
votes
2answers
2k views

How to change coordinates of a differential operator?

I'm doing a basic quantum mechanics problem and am trying to learn how to do it in Mathematica. Any help would be much appreciated. $\vec{L} = \vec{x} \times \vec{p}$ where $\vec{x}$ has components:...
33
votes
3answers
771 views

Is there a comprehensive list of functions with operator forms?

As of version 10, Mathematica sports operator forms for many functions like Map, SortBy, ...
13
votes
4answers
2k views

Exponential of a Differential Operator

In Mathematica, is it possible to exponentiate a differential operator such that the operator will act on a function, $f(x,p)$? Specifically, I wondering if I can get Mathematica to do this: $\exp(c\...
12
votes
2answers
341 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}=...
7
votes
2answers
330 views

HoldForm[Operator ##] on some list

Recently in response to this question Mr.Wizard suggested an unusual way to summing numbers. This doesn't seem to be documented. ...
7
votes
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 ...
23
votes
11answers
2k views

Generating an ordered list of pairs of elements from ordered lists

I have a pair of ordered lists. I want to generate a new ordered list (using the same ordering) of length n by applying a binary operator to pairs of elements, one from each list, along with the index ...
9
votes
2answers
6k views

Defining quantum-mechanical Bra and Ket operations

I have the following ket in the Fock basis: $\vert3, 0 ,1\rangle$, where each entry defines the number of photons in a particular mode and can take any one of the following numbers: 0, 1, 2, 3. As a ...
12
votes
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 ...
20
votes
4answers
850 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, ...
12
votes
2answers
250 views

Custom operator form for system functions?

There are some functions for which an operator form would make sense but isn't implemented. For example, I'd like to make this work: RandomSample[3] @ Range[10] ...
7
votes
2answers
7k views

How to find (numerical) value of a derivative at point?

I have the following function: f[0, 0] = 0 f[x_, y_] := Exp[-(x^2 + y^2)^(-1)] How do I find its partial derivatives at any given point, including $(0,0)$? This ...
10
votes
2answers
3k views

How do I expand a sum?

I have a problem with Mathematica's symbolic manipulations. As an example, consider the following expression: $$\sum _{i=1}^n -2 x_i \left(-a x_i-b+y_i\right)=0$$ How do I get Mathematica to expand ...
7
votes
2answers
766 views

How to make a binary function associative? (Or define an n-ary function?)

Suppose I have a simple function that I assign to an operator f[a_, b_] := a + b CirclePlus = f Then I want to write ...
3
votes
1answer
336 views

Custom operators; custom pattern matching with pure functions

What I'm trying to achieve in Mathematica is the creation of a binary operator whose operands are both pure functions over the natural numbers. The result of the operator should be another pure ...
8
votes
4answers
505 views

Change Operator Precedence of --> operator

I am trying to use --> operator with highest precedence ...
6
votes
3answers
935 views

Computing with matrix differential operators

I am looking the achieve a working set of Mathematica functions that would allow me to take products, commutators, etc. of (2x2) matrix differential operators and apply them to vector-valued functions ...
17
votes
2answers
1k views

What happens when you divide by ##?

I've been playing around with sequences a bit. In particular with using ## with unary and binary operators. Let's start simple, the following all make some kind of ...
3
votes
2answers
543 views

Polynomial expansion of operator

I am new to Mathematica, I am trying to generate the polynomial function of a operator. So for example, the operator $L $ is $\frac{\partial f}{\partial x}+\frac{\partial f}{\partial y} $, and I want ...
3
votes
1answer
389 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 ...
7
votes
1answer
584 views

Define an operator with the distributive property

I would like to define the operator with distributive, associative, and commutative properties - so that Mathematica can symbolically simplify expressions I use ...
3
votes
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 ...
7
votes
5answers
614 views

How to write an operator that acts on pure function (to give another pure function)

I would like to write an operator oper that acts on a pure function f with an undetermined number of arguments, with the syntax <...
10
votes
2answers
387 views

Change associativity of the @ operator

The @ operator in Mathematica is right-associative by default, i.e. f@g@h evaluates as f@(g@h) Is it possible to make the ...
4
votes
2answers
385 views

Question on operator: // N

I've seen a notebook with the following: ...
4
votes
1answer
649 views

Proof of the Dirac-$\gamma$ matrices identity

Given the matrices $\gamma_{k}=\begin{bmatrix} O & -i\sigma_{k}\\ +i\sigma_{k}& O \end{bmatrix}$ where $\sigma_{k}$ is the $k^{th}$ Pauli matrix $\gamma_{4}=\begin{bmatrix} I^{2} &0 \...
4
votes
1answer
171 views

Operator-Input Form for Lists?

The documentation on Operator-Input Forms shows the following example which suggests that there is an alternative, convenient, operator-style, tidy technique for inputting lists. However, there is ...
15
votes
2answers
2k views

How to define a non-standard algebra in Mathematica?

I want to define an algebra, where there are three elements: 0, 1 and $\infty$ and two operations, addition and multiplication defined, both commutative: $$\begin{align*} 0+0&=0\\ 0+1&=1\\ ...
14
votes
2answers
443 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 $f$, ...
8
votes
1answer
172 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 ...
5
votes
1answer
1k views

I want to be able to define (a(x) d/dx + b(x))^n

I want to be able to define an operator $(a(x) d/dx + b(x))^n$ where $d/dx$ is the derivative operator and $a(x)$ and $b(x)$ are known functions and $n$ is a positive integer. Related Query: How ...
10
votes
3answers
461 views

Operate over list of pure functions

I have list of pure functions (All functions are InterpolatingFunction) i.e {{a, b}, {c, d}, {e, f}, ...} and I would like ...
9
votes
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}...
9
votes
2answers
244 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 ...
7
votes
1answer
495 views

How to construct custom operators with precedence?

I need to combine data structures in operations analogous to addition, subtraction, multiplication and division (and more). I need more than one operation of each type, i.e. more than one method of ...
5
votes
1answer
295 views

Factoring a differential equation into an operator product

Following the fundamental theorem of algebra, I can (as stated here in Sec. 1.1.4) factor an $n$th-order linear ordinary differential equation $$ a_n \frac{d^n x}{dt^n} + a_{n-1} \frac{d^{n-1} x}{dt^{...
5
votes
2answers
522 views

How best to write an exponential of differential operators?

I want to evaluate a term like this, $$\left.\exp\left({1\over 2}\sum_{i,j=1}^{n}(A^{-1})_{ij}{\partial \over \partial x_i}{\partial \over \partial x_j}\right) f(\vec{x})\right|_{\vec{x}=0}$$ and I ...
3
votes
2answers
1k views

Differential operator squared

I defined a one-dimensional momentum operator $\hat{p}=-i\hbar\frac{\partial}{\partial{x}}$ in Mathematica p = -I * h * D[#, x]& and I want to get the ...
2
votes
1answer
387 views

Operator operation

There are two basic operators r={x,y,z} and p=-I*h*{D[#,x] , D[#,y], D[#,z]} &. The angular momentum operator is defined as $...
2
votes
1answer
163 views

Operator product

I have this problem: I define the gradient operator as: gradiente = {D[#, x] &, D[#, y] &, D[#, z] &} Now, if I want to apply the operator on a ...
4
votes
1answer
238 views

Products of Differential Operators

I have a differential equation defined as the product of operators which I want to expand out into a polynomial in powers of $z\frac{d}{dz}$ $\qquad \prod_{n=1}^p(z\frac{d}{dz}+a_n)$ However when I ...
3
votes
1answer
172 views

Extract differential operator from differential form

Let's say I have : a*u''[x]+b*u'[x] where a and b are constant I would need to get <...
3
votes
3answers
160 views

How make D[f,x] treat OverBar[x] as a constant

I have an expression of the form f = a*x +OverBar[x], where OverBar[x] is just a name, it has not much to do with the variable x. I want ...