# Questions tagged [quantum-states]

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### How to translate from a state/density matrix formalism to matrix product state representation?

From what I understand, MPS is just a simpler way to write out a state, compared to the density matrix. But how do I get those $A_i$ matrices? From all the examples I read, people just somehow "...
5answers
378 views

### Eigenstates/vectors of the sum of non-commuting Hamiltonians

Suppose I have two Hamiltonians $H_1$ and $H_2$, and they're both two-level systems (they do not commute, such as pauli $X$ and $Z$). $H_1$ has eigenstates $|\psi_{11}\rangle$ and $|\psi_{12}\rangle$, ...
1answer
127 views

### Why quantum mechanics uses density operators instead of probability distributions over state space?

Whenever I try to get my head around mixed states I am referred to the notion of density operators. I think that density operators were introduced to represent mixed states as operators. For what I ...
2answers
42 views

### Parameterizing a unitary transformation between pure states and viewing it as a rotation [closed]

Let $\vert\psi\rangle$ and $\vert\phi\rangle$ be pure states. Then there exists some unitary $U_t$ such that $U_t\vert\psi\rangle = \vert\phi\rangle$. I have a geometric picture in my mind but I'm not ...
2answers
59 views

### Why $\frac{1}{E-H_0+i\eta}|n\rangle \stackrel{?}{=} \frac{1}{E-E_n+i\eta}|n\rangle$?

A Hamiltonian $H_0$ is diagonalized in $\{|n\rangle\}$ i.e. $H_0|n\rangle=E_n|n\rangle$. Why can we write $$\frac{1}{E-H_0+i\eta}|n\rangle \stackrel{?}{=} \frac{1}{E-E_n+i\eta}|n\rangle$$ $H_0$ is in ...
1answer
44 views

### Energy Eigenstate of a Hamiltonian

What exactly are energy eigenstates? For something like H = $h\omega \left( \begin{matrix}1 & 2i \\-2i & 4 \end{matrix}\right)$ , what the eigenstates be like the eigenvectors, so $(i\,\,\,2)$ ...
3answers
120 views

### What is the meaning of the ket states in the notation $\langle x_f,t_f|x_i,t_i\rangle$?

Path-integral amplitudes are denoted by the inner product $\langle x_f,t_f|x_i,t_i\rangle$ where $|x_i,t_i\rangle$ is a time-independent position eigenstate of the time-dependent Heisenberg picture ...
1answer
154 views

### Is unphysical states still unphysical in an interaction theory?

Maggiore A modern introduction to quantum field theory Section 4 : In free quantum electromagnetic field theory... since only the two degree of freedom transverse wave, the energy, and the momentum, ...
0answers
55 views

### QFT - Bra-ket notation and correct operator interpretation

I'm taking a course in Quantum Field Theory and I'm having hard times understanding the notation adopted. Let me be more precise. Considering the Lagrangian for the (classical) real scalar field [...
2answers
95 views

### Difference between normalized wave function and orthogonal wave function?

I am confused about when we say that a wave function is NORMALIZED so that we say that the indefinite integral of the wave function squared = 1, vs. when we say that the wave function represents ...
0answers
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### Quantum numbers for diatomic molecules

A diatomic molecule: is always symmetric if we rotate it along its internuclear axis. Let it be the z-axis. Then we can say that $[{\cal \hat H}, {\hat L}_z] =0$, so there is a common set of ...
1answer
40 views

### Eigenvalue of a vector in a subspace [closed]

Consider, a quantum system has a hamiltonian with eigenstates $\{|\phi_1\rangle,|\phi_2\rangle,|\phi_3\rangle\}$ and associated eigenvalues $\{\lambda_a,\lambda_a,\lambda_b\}$. My notes state that any ...
1answer
51 views

### Understanding how to determine the time evolved state vector for a unitary operator constructed from non-commutating operators

Suppose we have a time independent hamiltonian $$H = \hbar g (\sigma_x + \sigma_y + \sigma_z)$$ I know that the unitary operator is as follows: $$U(t) = exp(-iHt/{\hbar})$$ Sinnce the pauli spin ...
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1answer
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### Why does the hamiltonian in the operator act on the wave function?

Suppose we have the following relation: $H_0 | \phi_1\rangle = E_1 |\phi_1 \rangle$ Why is it that if we take the unitary function $$U_{0} = \exp\left(\frac{-iH_{0}t}{\hbar}\right)$$ and apply it to ...