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Questions tagged [quantum-mechanics]

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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Doubt on Sakurai's proof of Wigner-Eckart theorem

In Sakurai's and Napolitano's book "Modern quantum mechanics" there's a nice proof of the theorem. This can be found also almost identical on Wikipedia's Wigner–Eckart theorem - Proof. The thing that ...
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Understanding the statement of the bandwidth theorem

I know that the Bandwidth Theorem (BT) and the Heisenberg Uncertainty Principle (HUP) are basically the same thing, and stem from the fact that for operators $A,B$, we have: $$\Delta A \Delta B \geq \...
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What is the nature of vibrational relaxation in fluorescence?

Electrons in fluorescent substances get excited from the ground state($S_o$) to the first excited state($S_1$) or higher excited states in case of upconversion. Depending on the statistical ...
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Why this is classical correlation and not full (classical + quantum) correlation?

Let a quantum system be given which has two subsystems $A$ and $B$ so that the Hilbert space decomposes $\mathscr{H}\simeq \mathscr{H}_A\otimes \mathscr{H}_B$. If the state of the system is $\rho$, ...
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Non-relativistic limit of particle decay

Let us consider the theory with scalar coupling $g\bar{\psi}\phi\psi$. For the decay process $\phi\rightarrow \bar{\psi}\psi$ one can write down the following amplitude: $$\mathcal{M}=ig\bar{u}(p_{-})...
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Impact of electronic binding energies on mass and acceleration

According to relativity, the inertial mass of an object that enters into the force equation to get acceleration is given by the total energy in the center of mass rest frame. $$E=Mc^2=\sum_i (m_i c^...
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Is the Moyal-Liouville equation $\frac{\partial \rho}{\partial t}= \frac{1}{i\hbar} [H\stackrel{\star}{,}\rho]$ used in applications?

This answer by Qmechanic shows that the classical Liouville equation can be extended to quantum mechanics by the use of Moyal star products, where it takes the form $$ \frac{\partial \rho}{\partial t}~...