Linked Questions

4 votes
2 answers
2k 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: ...
RaymartJay's user avatar
1 vote
2 answers
520 views

Writing (differential) operators [duplicate]

I would like to apply the differential operator $- (\partial_\theta -\frac{i}{\sin (\theta)} \partial_\phi + s \cot (\theta))$ to a function $F$ (Spherical Harmonics), which is dependent on $\theta$ ...
Gladaed's user avatar
  • 987
0 votes
1 answer
290 views

Differential equations expressed in operator form [duplicate]

Is it possible to make a workable operator representation of differential equations in Mathematica? I think it would make solving my differential equations easier, but I have no idea how to do it. ...
user12991's user avatar
1 vote
1 answer
593 views

How to compute the composition of linear differential operator [duplicate]

For example, I have to write down the differential operator below as a polynomial in $\partial$ $$(\partial-f_n(x))(\partial-f_{n-1}(x))\cdots(\partial-f_1(x))$$where the product the the composition. ...
Nirvanacs's user avatar
  • 117
1 vote
0 answers
31 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 ...
Uwe.Schneider's user avatar
19 votes
2 answers
21k views

How to define a differential operator?

I have a linear differential operator, for instance, $L\left (\partial _{t} \right )=\partial _{tt} - 3\partial _{t} + 2$. I use it in 2 different ways: apply the operator to a function: $L\left (\...
prazuber's user avatar
  • 429
17 votes
2 answers
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\\ ...
Anixx's user avatar
  • 3,585
5 votes
4 answers
7k 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+...
QuantumDot's user avatar
  • 19.7k
16 votes
2 answers
2k views

Pull out scalars from NonCommutativeMultiply in commutator of SU2 spin algebra

I am trying to work on spin chains in Mathematica. That is, N spin-1/2 on a one-dimensional lattice with periodic boundary condition (N+1=1). I need therefore the SU2 spin algebra $S_z, S_+, S_-$ with ...
user50473's user avatar
  • 579
8 votes
3 answers
5k 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 ...
TehHO's user avatar
  • 109
7 votes
3 answers
516 views

Iterated differential operator

I would like to implement the following differential operator in Mathematica, $$ \prod_{j=1}^n \left({\mathrm d \over \mathrm d x}-j\right) $$ On a case by case basis, I can just expand it out and ...
B. Erenu's user avatar
11 votes
5 answers
254 views

How can I translate a MathWorld statement into Mathematica syntax?

The Wolfram Mathworld has the following statement here: A derivative identity for expressing higher order modified Bessel functions in terms of $I_0(x)$ is $I_n(x)=T_n(d/(dx))I_0(x)$ However, I'm ...
Hedgehog's user avatar
  • 624
6 votes
3 answers
1k 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 ...
Vincent's user avatar
  • 63
5 votes
1 answer
2k 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 ...
Quasar Supernova's user avatar
3 votes
2 answers
2k 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 ...
arax's user avatar
  • 1,831

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