Linked Questions

0
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2answers
356 views

Tensor product postulate [duplicate]

Non relativistic quantum mechanics assumes that a composite system should be described with the tensor product of the component systems. This is the tensor product postulate of quantum mechanics. I ...
0
votes
1answer
464 views

Why tensor product? [duplicate]

Let $A$ an $B$ be two discrete observables (like spins). When exactly and why we have to consider their tensor product when talking about the mutual observation of the corresponding phenomena?
0
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1answer
164 views

Quantum spin, tensor product: a long time relationship [duplicate]

Anyone who has studied quantum mechanics know the following relation: $ 2 \otimes 2 = 3 \oplus 1 $ But how did a man woke up and said "Hell yeah, I'll use tensor product of two spin $1/2$ to simulate ...
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0answers
114 views

Why are systems joined via a tensor product? [duplicate]

This question comes from seeing that the triangle addition rule for quantum mechanics comes out of groups/representation theory; I thought this was odd as we haven't used any group ideas in QM up to ...
0
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0answers
23 views

Why are many variable probability distribution described by a Tensor product? [duplicate]

Why are many variable probability distribution described by a Tensor product? I am asking this question because i came to know that wavefunction $\psi(x,y)$ is a tensor product of two copies of $\psi(...
19
votes
4answers
13k views

How to tackle 'dot' product for spin matrices

I read a textbook today on quantum mechanics regarding the Pauli spin matrices for two particles, it gives the Hamiltonian as $$ H = \alpha[\sigma_z^1 + \sigma_z^2] + \gamma\vec{\sigma}^1\cdot\vec{\...
15
votes
2answers
4k views

Tensor product in quantum mechanics?

I often see many-body systems in QM represented in terms of a tensor products of the individual wave functions. Like, given two wave functions with basis vectors $|A\rangle$ and $|B\rangle$, belonging ...
5
votes
2answers
3k views

Tensor Product vs. Direct Product for three spin-1/2 particles

Let us consider three spin-1/2 particles and only focusing on their intrinsic spin $S$. The Hilbert space has then to be $\mathcal H = ℂ^2 ⊗ ℂ^2 ⊗ ℂ^2$. The spin can be described by $V ∈ \text{SU(2)}$ ...
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votes
2answers
2k views

Importance of Kronecker product in quantum computation

To get product state of two states $|\phi \rangle$ and $|\psi \rangle$, we use Kronecker product $|\phi \rangle \otimes |\psi \rangle$. Instead of Kronecker product $\otimes$, can we use Cartesian ...
7
votes
4answers
775 views

How do tensor products and direct sums fit into quantum mechanics?

I understand that at times tensor products or direct sums are taken between Hilbert spaces in quantum mechanics. I don't, however, know when this can be done or when it should be done. I would like ...
2
votes
2answers
2k views

Hamiltonian of Harmonic Oscillator with Spin Term

We have the usual Hamiltonian for the 1D Harmonic Oscillator: $\hat{H_{0}}=\frac{\hat{P^2}}{2m} + \frac{1}{2}m \omega \hat{X^2}$ Now a new term has been added to the Hamiltonian, $\hat{H} = \hat{...
3
votes
2answers
748 views

Indistinguishability in Quantum Mechanics

When describing the defining characteristics of bosons and fermions, I have a problem with the idea of "label switching" - whereby you have the wavefunction for two particles and the particles' labels ...
2
votes
3answers
691 views

Tensor product states in QM

In QM, we use tensor products to construct the vector space of the states of a multi-particle system - but that construction doesn’t seem to have a counterpart in classical mechanics. In QM, it seems ...
0
votes
1answer
627 views

Wavefunction of a system of particles

A three-dimensional volume $V$ contains a certain number $N$ of electrons and they can't escape the volume $V$. Assume for simplicity that the potential $\mathcal{V}(\mathbf{r})$ is zero in all the ...
3
votes
2answers
346 views

Tensor product in many electron atoms

One of the quantum mechanics postulates states that a composite system can be described with the tensor product of the component systems. I've read some rationalization about this fact in some post ...

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