Linked Questions
11 questions linked to/from Pull out scalars from NonCommutativeMultiply in commutator of SU2 spin algebra
39
votes
6
answers
8k
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 \...
- 1,581
12
votes
2
answers
13k
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 ...
- 997
12
votes
3
answers
3k
views
Is there a way to do Quantum Computing in Mathematica notebook?
I saw 2 efforts in that direction: WSS17 and WSS16, but I am not sure if there is something in the latest Mathematica that actually allows users to simulate quantum gates.
Can anyone please point me ...
- 599
12
votes
1
answer
1k
views
multiplication of vector spaces
Original Question
Disclaimer: The question motivated by the product of Hilbert spaces which arises from separate degrees of freedom which a system might contain in quantum technical system.
Examples ...
- 601
4
votes
1
answer
2k
views
Hadamard Lemma and commutators algebra
I would like to implement the following formula, which goes under the name of Hadamard Lemma:
$ e^A \, B \, e^{-A} = \sum_{k=0}^{+\infty} \frac{1}{k!} [A,B]_k $
where
$ [A,B]_0 = B , \...
- 269
1
vote
1
answer
382
views
Convert, using the Pauli matrices, an $n \times m$ matrix of quaternions into a $2 n \times 2 m$ matrix with complex entries, and vice versa
I'd like to go between $n \times m$ matrices with quaternionic entries to (using, it would seem, the Pauli matrix conversion scheme) to $2 n \times 2 m$ matrices with complex entries, and vice versa. ...
- 2,385
2
votes
1
answer
768
views
Multiply out product of sums
For a specific quantum mechanical problem I need to multiply out operators in order to calculate a trace by hand. For example I need a Hamiltonian squared with $H^2$. The Hamiltonian contains of a few ...
- 842
2
votes
0
answers
685
views
Outer product using the quantum mathematica package
I am using the quantum Mathematica package and am trying to do computations that require me to use the outer (tensor) products of Pauli matrices. I would define this as, for example, ...
- 21
1
vote
1
answer
273
views
Forming Kronecker products for "non-adjacent" vector spaces
In quantum mechanics, we often want to build operators acting on multiple particles by simply "Kronecker-ing" operators from the single-particle spaces. That is, if I have some matrix $A$ acting on ...
- 667
0
votes
0
answers
207
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
3
votes
0
answers
98
views
Pattern Matching and overloading NonCommutativeMultiply [duplicate]
My goal right now is to implement some rules like linearity etc for noncommuting operators (arbitrary matrices etc). This is partly an exercise for me to understand MMA better so giving me a package ...
- 852