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Results tagged with quantum-mechanics
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user 21712
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.
3
votes
Accepted
Schrödinger equation for a harmonic oscillator
First of all you should recall that Schroedinger equation is an Eigenvalue equation. If you are unfamiliar with eigenvalue equations you should consult any math book or course as soon as possible.
An …
- 404
5
votes
Accepted
Proof for commutator relation $[\hat{H},\hat{a}] = - \hbar \omega \hat{a}$
Start with your $\hat{H} = \hbar \omega \left( \hat{a}^\dagger\hat{a} + \frac{1}{2} \right)$. I will omit hat notation from this point. The commutator then reads as
\begin{equation}
\left[ H, a \right …
- 404