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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.
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Moving from eigenstate basis of a Hamiltonian back to operator basis [duplicate]
This is maybe a stupid question but one I have been bugged by a long time.
How to translate back from an eigenstate basis to another operator-basis.
Let me give an explicit example to show what I am …
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Explaining why $\mathrm{ d/d}x$ is not Hermitian, but $\mathrm{i~ d/d}x$ is Hermitian
What operators are hermitian depends on what type of inner product you have in your Hilbert space and what the boundary conditions are.
If your inner product is defined as $\langle\phi|\psi\rangle:=\ …
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Reference guide for standard descriptions of materials
Is there any reference that has a coherent list of materials and what type of approximate Hamiltonian to best describe them with (where it is known). Particularily I am looking for the following bits …
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Examples of Complex valued wave functions
First and foremost if you take a Harmonic oscillator and try to find the time dependent wavefunction you necessarily get a complex phase factor $\lvert n\rangle \to e^{-i\hbar^{-1}E_nt}\lvert n\rangle …