IGNOU BPHET 141 2026 - 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) = \frac{1}{2} m \omega^2 (-x)^2 = \frac{1}{2} m \omega^2 x^2 = V(x), ] so

______ _____ _______ _____ _________ ________ ____ ___ ______ _____ _________ __________.
_______ _______ _______ ________ ___.
___ ___ ___ _________ _________ _______ ___ ________ _________ _________ ___.
______ ____ ________ ____ ________ _____ _____ ________ ___ _________ ______.
______ _____ _____ ______ ______ __________ _______ _________ ______ ______ _________ ____.
_______ _______ ___ __________ ___ ______ ______ _______ __________ _____ ________.
_______ __________ _______ __________ ____ _________.
________ _____ ______ ____ _______ _____.
__________ ___ ____ ____ __________ _____ _______ ____.
__________ ________ _________ ______ ________ _________ _________ ____ _______ _______.
________ ____ _______ ________ _________ _______ _____ ___ ____ _____ _______ ___.
__________ ______ __________ _______.

IGNOU ACADEMY

Your IGNOU journey, made easier.