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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.

9 votes

Angular orientation of exact solution of the Hydrogen Schrödinger Equation

We can find a nice visual representation of the Spherical Harmonics in this wiki article. You can see that in fact, only $l=0$ is spherically symmetric. We know that: The ground state is the only tr …
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6 votes
Accepted

What does it mean to take the "trace" of a function?

First of all, I think it is important to you to know that they cite this equation as being the equation 24 of a broken link reference, which is the paper Langreth, D. C., Dion, M., Rydberg, H., Schrö …
Ruffolo's user avatar
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6 votes

Is there a real-valued formulation of the Pauli equation

Is there are standard approach to this that yields something analogous to the quantum potential in the Schrodinger equation case? You should check the book The Undivided Universe, by D. Bohm and B.H …
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5 votes
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Aharonov-Bohm using density matrix?

I think there would be no dificulties here. For example, in the Aharonov-Bohm effect studied in a Young Interferometer with a solenoid placed between the slits, we describe the input state (before sol …
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5 votes
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Why do we say $E=hf$ supports particle nature of light?

which supports the particle nature of light. In fact, it doesn't. First, Planck's law is not only about this mathematical relation, but it includes a discretization process. The density of modes per …
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4 votes

Why is an unpolarized beam considered an incoherent mixture of equal weights?

The best way to understand polarization coherence is through the Poincare Sphere. When we deal with polarized light, the approach for perfect coherent beams is to describe polarization using the polar …
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4 votes
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Joint distribution of possible eigenvalues when applying two commutating operators

I think the good comments of @TobiasFünke and the good answer of @hft already showed the missing point, but I want to give you two examples. Ex. 1: No degeneracy Consider the matrices (I'll consider f …
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4 votes
1 answer
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Is the Classical limit of Quantum theory the Newtonian Mechanics?

Recently I started to study Quantum Dissipative models like Caldeira-Leggett model and it occurs to me that this model provides a Quantum to Classical transition, but the Classical resultant system sa …
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4 votes

Could probability amplitude for a path equal a complex number whose length is always 1 and w...

Consider a particle travelling from $x_i$ to $x_f$. Quantum mechanically, we could ask about the probability to have such process $$ p(x_i\rightarrow x_f) = |\langle x_f|\Psi(t)\rangle|^2 = |\langle x …
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4 votes
Accepted

Precise form of two-mode squeezed state

For me, it sounds a specific choice for the phase $\varphi$, since $e^{i\varphi}$ also disappeared. Look that if $\xi = re^{i\varphi}$, for $\varphi = \pi$ we have real $\xi$ and $(-1)^n e^{in\pi} = 1 …
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3 votes

Why do people say the dynamics of quantum mechanics is always linear?

The linearity of quantum comes from The Principle of Superposition and is one of the most fundamental ideas in Quantum Theory. In the book "The Principles of Quantum Theory" chapter I, Paul Dirac argu …
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3 votes
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Are the eigenstates of an electron in the hydrogen atom coordinate dependent?

There is an elegant way to check how will be the new eigenfunctions of the changed Hamiltonian. A change of origin is equivalent to a displacement of the system. Such transformation could be represent …
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3 votes

Possible errata Landau and Lifshitz in $\S29$ Matrix elements of vectors in Quantum Mechanic...

I don't know what is wrong with your reasoning, since it seems to return the right result in the special case where $A_{yy}=A_{zz}$. That said, I never saw this approach, and I searched in Landau'book …
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2 votes

What does the absence of a ground state physically mean?

Consider a Hamiltonian bounded from below. If there is no ground state, any state will not be the lowest energy state, which means that it could suffer a transition to a lower energy state. We can bui …
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2 votes

Do maxwells equations describe the probability (conjugate squared wavefunction) distribution...

The quantum theory of light was developed to describe phenomena that cannot be described by Maxwell equations. If both theories were complete equivalents, there would be no reason to develop QED or qu …
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