Determine the wave function and energy of the ground state and first excited state for a system of two identical bosons in 1D simple harmonic oscillator.
For a 1D simple harmonic oscillator (SHO), the single-particle Hamiltonian is [ \hat{H} = \frac{\hat{p}^2}{2m} + \frac{1}{2} m \omega^2 \hat{x}^2 ] with energy eigenvalues and eigenfunctions: [ E_n = \left(n + \frac{1}{2}\right)\hbar \omega, \quad n = _________ ____ ____ ______ _______ ______ _____ ______ _________ __________.
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A charged particle of mass m and charge q, is confined to a one-dimensional box of side L with . At t > 0, an electric field
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$
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and
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;
, and E2 > E1. The system is subjected to a time-dependent perturbation:
.
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at
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Determine the wave function and energy of the ground state and first excited state for a system of two identical bosons in 1D simple harmonic oscillator.
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