List questions from quantum-mechanics

Published on 26 Mar 2026 - 12:35

35

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Introducing internal spin into the mechanical equations of an orbiting particle

Published on 27 Mar 2026 - 0:03

91

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Complex extension of the Stone - von Neumann Theorem?

Published on 18 Feb 2024 - 22:11

50

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Schmidt decomposition in larger Hilbert spaces

Published on 26 Mar 2026 - 12:40

57

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Compute a quantum state $\rho$ corresponding to an ensemble

Published on 26 Mar 2026 - 9:38

61

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Find an ensemble consisting of three distinct pure states that correspond to the same mixed state

Published on 26 Mar 2026 - 7:59

75

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Show that a state $\rho=\sum_i p_i|e_i\rangle\!\langle e_i|$ has purifications of the form $\sum_i s_i |e_i\rangle\otimes|f_i\rangle$

Published on 26 Mar 2026 - 8:02

50

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trouble with a change of basis

Published on 26 Mar 2026 - 14:24

60

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Prove that a change-of-basis map is an isometry between complex hilbert spaces, to prove uniqueness of purifications

Published on 26 Mar 2026 - 14:21

46

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The time-derivative of the Hamiltonian for a 1D harmonic potential

Published on 30 Mar 2026 - 20:42

54

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If $ρ_{AB} ∈ D(H_A \otimes H_B)$ such that $ρ_{A}$ is pure. $\implies ρ_{AB} = ρ_{A} \otimes ρ_{B}$

Published on 26 Mar 2026 - 8:00

35

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$0 ≤ A ≤ I. $ $\iff$ ⟨ψ|A|ψ⟩ ∈ [0, 1] for every unit vector $|ψ⟩ ∈ H$

Published on 26 Mar 2026 - 11:03

54

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On the mathematics behind the Dyson Series

Published on 27 Feb 2024 - 15:44

62

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Why harmonic functions does not belong to basis while it's eigenvector of Laplacian operator?

Published on 02 Mar 2024 - 19:15

33

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If $\rho_{AB}$ is a separable then the partial transpose w.r.t to A is PSD

Published on 26 Mar 2026 - 9:42

List Question

Outer product as an operator in an infinite Hilbert space

Introducing internal spin into the mechanical equations of an orbiting particle

Complex extension of the Stone - von Neumann Theorem?

Schmidt decomposition in larger Hilbert spaces

Compute a quantum state $\rho$ corresponding to an ensemble

Find an ensemble consisting of three distinct pure states that correspond to the same mixed state

Show that a state $\rho=\sum_i p_i|e_i\rangle\!\langle e_i|$ has purifications of the form $\sum_i s_i |e_i\rangle\otimes|f_i\rangle$

trouble with a change of basis

Prove that a change-of-basis map is an isometry between complex hilbert spaces, to prove uniqueness of purifications

The time-derivative of the Hamiltonian for a 1D harmonic potential

If $ρ_{AB} ∈ D(H_A \otimes H_B)$ such that $ρ_{A}$ is pure. $\implies ρ_{AB} = ρ_{A} \otimes ρ_{B}$

$0 ≤ A ≤ I. $ $\iff$ ⟨ψ|A|ψ⟩ ∈ [0, 1] for every unit vector $|ψ⟩ ∈ H$

On the mathematics behind the Dyson Series

Why harmonic functions does not belong to basis while it's eigenvector of Laplacian operator?

If $\rho_{AB}$ is a separable then the partial transpose w.r.t to A is PSD

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