Explain whether the eigen functions of the following Hamiltonian for a

Question

Explain whether the eigen functions of the following Hamiltonian for a particle of mass m will have a definite parity: $H = \frac{p^2}{2m} + \frac{1}{2}m\omega^2x^2$ .

19 Jan 2026

Answer :

Word Count : 161

The given Hamiltonian is [ H = \frac{p^2}{2m} + \frac{1}{2} m \omega^2 x^2, ] which is the standard one-dimensional harmonic oscillator. The potential energy term is [ V(x) = \frac{1}{2} m \omega^2 x^2. ] This function satisfies [ V(-x) = ____ ___ ____ ______ __________ _______ _________ ________ ___ ____ _________ ____.
_____ _____ ______ _____ _________ ______ ____ _______.
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___ ______ ____ ______ ______ ___.
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