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Results tagged with quantum-mechanics
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user 113077
Quantum mechanics describes the microscopic properties of nature in a regime where classical mechanics no longer applies. It explains phenomena such as the wave-particle duality, quantization of energy, and the uncertainty principle and is generally used in single-body systems. Use the quantum-field-theory tag for the theory of many-body quantum-mechanical systems.
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QM sytem with eigenvalues of the form $f(m*n)$ and prime number gap spectrum
Depending on the dimension and the symmetry and form of the potential, the energy eigenvalues of a quantum mechanical system have different functional forms. Eg. The particle in the 1D-box gives rise …
2
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1
answer
655
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QM Continuity Equation: many-electron in the magnetic field version?
In 1-particle non-relativistic QM we have the continuity condition as a per definitionem property for the 1-electron probability current density for an electron in the magnetic field in a stationary s …
3
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1
answer
166
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Consecutively measuring $\hat{s_x}^2$, $\hat{s_y}^2$ and $\hat{s_z}^2$ of a spin 1 particle,...
I am hearing a lecture from John Conway on the free will theorem. This is more or less a purely mathematical theorem (with physical consequences). But it is so since Conway and Kochen deliberately sep …
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0
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47
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Is (energetic) degeneracy a physical property?
In quantum mechanics, observable properties correspond to expectation- or eigenvalues of (hermitian) operators.
After measurement (of an eigenvalue) the system is in an eigenstate that corresponds to …
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1
answer
537
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Hamiltonian-commutation, hermiticity and non-hermiticity (QM)
When we have a QM system in an energy eigenstate (say after a measurement of energy) then we can measure any time another quantity that is described by an hermitian operator that commutes with the Ham …
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0
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55
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(When) Can the mechanical (kinematic) momentum density ($n$-particle QM, non-rel) become zero?
I am investigating quantum mechanical $n$-electron mechanical (kinematic) momentum densities in molecular systems by numerical methods. For a $n$ electron state function $\Psi$, non-relativistic case …
3
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1
answer
252
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Gauge-independence of the "$n$-particle" probability current
Problem
Show for the non-relativistic quantum mechanical problem of $n$ electrons in a static homogenous magnetic field $\bf B$ and ignoring spin that the probability current density is gauge indepen …
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152
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Explicit form for operators representing the integrals of motion in quantum mechanics
Is there any way to derive the quantum mechanical operators that form the integrals of motion in quantum mechanics from the Hamiltonian for general systems?
Let's for simplicity focus on stationary pr …
2
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2
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252
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Analogous structure of Diffusion and Schrödinger equation and definition of flux?
I came across some analogous structure of diffusion and the quantum mechanical particle (Schrödinger eq.). I have seen that there have been similar questions asked, but the (probablitily flux and the …
3
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0
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726
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Perturbation theory development for the ground state of the QM particle in the box with a ce...
In the course of a discussion in the chat there emerged an interesting problem, namely a particle in an infinite well with an additional Dirac-delta function spike of scalable hight:
$$
H = -\frac{\hb …
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2
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113
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Why goes $i\rightarrow-i$ under $\mathcal{PT}$-transformation?
Question in the title.
What I understand is that under $\mathcal{PT}$ reversal $\hat{p}\rightarrow\hat{p}$ and $\hat{x}\rightarrow-\hat{x}$ and then since the commutation $[\hat{x},\hat{p}]=i\hbar$ " …
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Spin Orbital Coupling matrix in $p$-orbital basis
For example look at entry 1,2:
$(H_{SOC})_{1,2} \,=\, <p_x\uparrow| H_{SOC} |p_x\downarrow>\,=\, <p_x\uparrow| \frac{\alpha}{2}(L^{+}\sigma^{+}+L^{-}\sigma^{-}+ L^{z}\sigma^{z})|p_x\downarrow> \,=\ …
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799
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Particle in a box plus step (ground state)
I am trying to come up with a QM problem that:
Can be solved analytically
Contains a potential that is a sum of some analytically solvable potential and another contribution: $V'=V_0 + V$
Is then a …
2
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0
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39
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Degree of degeneracy of energy levels and irreducible representations of Hamiltonian symmetr...
In case the Hamiltonian of a system has some non-trivial symmetry regarding the physical space, let's assume symmetry that can be described by a finite symmetry group (e.g. a point group symmetry) one …