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Questions tagged [quantum-mechanics]

For questions on quantum mechanics, a branch of physics dealing with physical phenomena at microscopic scales.

Quantum mechanics, also known as quantum physics or quantum theory, deals with classical physical phenomena at quantum scales.

The precise nature of the subject has changed over the years. This article explains its current formulation.

Quantum mechanics aims toprovide a mathematical description of the dual particle-like and wave-like behaviors and interactions of energy and matter.

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How is the determinant of the correlations block a symplectic invariant in a covariance matrix

A well-known result is that every two-mode covariance matrix $$ \sigma_{AB} = \pmatrix{\alpha & \gamma \\ \gamma^T & \beta} $$ can be transformed via a symplectic transformation into a standard form with all diagonal 2 × 2 subblocks, $\alpha =…
Kiro
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Two-particle operator in the second quantization

In "Quantum mechanics" by Schwabl I found a chapter (1.3.3) about one- and two-particle operators in the second quantization. The derivation was only sketched and contained this equation: $\sum_{\alpha \neq \beta} \left|i\right\rangle_\alpha…
alkamid
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the evolution of spin in the Heisenberg picture of Quantum Mechanics

Assuming that the operators σi describe the component i of the spin observable for a spin- 1 2 particle, and assuming this particle to be immersed in a time-independent magnetic field B~ such that the Hamiltonian of the system is given by …
italy
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Incident beam above a potential well

I have the question: Consider a beam of particles of mass $m$ and energy $E>0$ incident from the right on the potential well $$ V(x) = \begin{cases} 0 & \text{if } x \leq 0\\ -V_0 & \text{if } 0
user141443
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Energy and momentum operator on the interval

Does there exists a common eigenbasis of the energy operator $T=p^2/2m$ and the momentum operator $p=-i\hbar\, d/dx$ for a particle in a 1-dimensional box of length $L$? Thanks in advance.
user229961
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Schrodinger equation to find general wave function

I am trying to answer this question: I have tried solving the Schrodinger equation using separation of variables. However in the later time wave function i can not seem to get the exp(-3i...) My current workings are:
Robert Thompson
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Approximation to series for quantum harmonic oscillator

For the function $$h(\xi) = C \sum \frac 1 {(j/2)!} \xi^j$$ Griffith's makes the following approximation at large $\xi$: $$h(\xi) = C \sum \frac 1 {(j/2)!} \xi^j \approx C \sum\frac 1 {j!} \xi^{2j} \approx C e^{\xi^2}$$ Any explanations how the…
Sidd
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Antilinear correspodence of bra and ket proof

I do not understand how the antilinear correspondence arises between ket vectors in V and bra vectors in V' (dual space): So I want to know why $$ \alpha\lt f_1 | + \beta\lt f_2 | $$ corresponds to $$ \alpha^* | f_1 \gt + \beta^* |f_2 \gt $$ where…
Ben Gunn
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Creating a Hermitian function

Say I have an operator $A$ such that $A^\dagger = B$. I want to construct a Hermitian function, $f$, of these operators, $f(A,B)^\dagger = f(A,B)$. Is it possible to construct a function $f$ such that $f$ is not a function of $A+B$?: $f(A,B)\neq…
Quantization
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Bloch vector time evolution in magnetic field

I'm wondering if there is a smart way of solving the system of equations $$\frac{d\vec{n}}{dt} = \gamma (\vec{n} \times \vec{B}(t)),$$ where $\vec{n}(t) = \big(x(t),y(t),z(t) \big)$ is the Bloch vector and $\vec{B}(t) = (B_1\cos\omega t, B_1 \sin…
Spine Feast
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Operators in Quantum Theory

Let $U$ be a unitary operator on a Hilbert Space, and let $\phi$ be an eigenvector of $U$ with eigenvalue $\mu$. Show that $|\mu|=1$ ? I know that if $U$ is unitary then $UU^{+}=UU^{-1}=I$ but I'm not really sure how to use it in this case?
sarahusher
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Quantum measurement - How does this commutator correspond to the following?

From the book Quantum Measurement by Vladimir B. Braginsky and Farid Ya.Khalili How do they go from 5.18 to 5.19?
user32462
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Observable compatibility

I'm reading Quantum Mechanics by Cohen-tannoudji and I find some parts not clear. a hermitian operator is observable if there exists an orthonormal complete basis or if every orthonormal system of the vector is a complete basis. it's linked to…
Alessandro Vagni
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In the context of QM, is it correct to say that the Dirac delta is like a continuous version of the Kronecker delta?

Thinking about observables, there is continuous observables such as position and discrete observables such as energy of an electron in an atom. For the discrete case, we have: Suppose we have a orthonormal basis {$|E_i \rangle $}, which means that…
Iberis
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How do you derive, the “naive form” of the Lippmann-Schwinger Equation?

I was looking for a derivation of the ‘Lippmann-Schwinger Equation’. The wikipedia material at http://en.wikipedia.org/wiki/Lippmann%E2%80%93Schwinger_equation#Derivation does not (23rd Jan 2024), as I understand matters, actually contain a…
user151522
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