Linked Questions
36 questions linked to/from Having the derivative be an operator
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:
...
- 53
1
vote
2
answers
560
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 $\theta$ ...
- 997
0
votes
1
answer
306
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. ...
- 71
1
vote
1
answer
605
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.
...
- 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 ...
- 251
20
votes
2
answers
22k
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 (\...
- 439
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:
$$\begin{align*}
0+0&=0\\
0+1&=1\\
...
- 3,712
5
votes
4
answers
7k
views
How to write a differential operator in Mathematica
I have a very basic question. I am trying to code the LHS of the differential equation:
$$\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+...
- 19.8k
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 ...
- 589
9
votes
3
answers
6k
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 ...
- 119
7
votes
3
answers
529
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 ...
- 81
11
votes
5
answers
256
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 ...
- 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 ...
- 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 ...
- 1,708
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 ...
- 1,851