Linked Questions
11 questions linked to/from Boson commutation relations
10
votes
1
answer
5k
views
How to implement ladder operators for the quantum harmonic oscillator?
I would like to write the annihilation and creation operators for the harmonic oscillator, and see how they act on basis states of the form $\lvert n\rangle$.
What's the best approach to implement ...
- 569
11
votes
1
answer
1k
views
Sorting function for non commuting bosons
I am trying to write a sorting function which will sort expressions involving products of bosonic objects which do not commute. For example, I can have objects like $a,\ a^\dagger,\ b,\ b^\dagger$ ...
- 505
6
votes
1
answer
1k
views
Normal ordering in Mathematica
I want to create a function which normally orders a string of field operators. Consider the following:
$$\langle0\vert\hat{a}(k_n) \cdots \hat{a}(k_2)\hat{a}(k_1)\hat{a}^\dagger(k_1)\hat{a}^\dagger(...
- 977
3
votes
1
answer
941
views
A product for fermionic variables
I'm trying to write a dot product that can handle fermionic variables, i.e., let $a,b$ be fermionic variables, $a\, b=-b\, a$.
There is already a package that can handle fermionic+bosonic variables, ...
- 86
0
votes
3
answers
596
views
Calculating bracket operations [closed]
Is there a way to calculate commutation relations in Mathematica? For example, let's say I want to compute ; how can this be done?
- 11
1
vote
1
answer
100
views
Rearrange the list with some rules
I am trying to solve physic problem on operators which are not commute. However, I am not good at coding, so I am having some problem with Mathematica code.
Let's define my list such that
...
- 1,780
1
vote
1
answer
141
views
normal ordering of Bose operators
Suppose I have lot of product terms of Bose operators, e.g:
...
- 648
0
votes
0
answers
146
views
Is it possible to perform the following computation in mathematica?
Consider the following defined commutation relations:
$$[\hat a,\hat a^{\dagger}]=1$$
$$[\hat b,\hat b^{\dagger}]=1$$
$$[\hat a,\hat b]=0$$
(where the usual algebra of commutators holds)
Let us now ...
- 226
2
votes
1
answer
51
views
NonCommutativeMultiply question- syntax question
if I define id as:
id /: NonCommutativeMultiply[id, x_] := x
id /: NonCommutativeMultiply[y_, id] := y
then ...
- 648
2
votes
1
answer
71
views
grouping common powers of Bose operators
I compute a product of Bose operators and turn it into normal ordering using Boson commutation relations, e.g:
...
- 648
0
votes
0
answers
80
views
Simplifying expression involving Boson operators
I want to do calculations involving Boson operators $a(k), a^{\dagger}(k)$, e.g $(x + a(k))(y+a^{\dagger}(k))$. My code is:
...
- 648