Introduction to Quantum Mechanics · Problem 8.5

The Variational Principle — David J. Griffiths

Physics — Quantum Mechanics · variational_bouncing_ball

Problem

Using a trial function of your own devising, obtain an upper bound on the ground state energy for the "bouncing ball" potential (Equation 2.185), and compare it with the exact answer (Problem 2.59): Egs=2.33811(mg2ℏ2/2)1/3E_{\text{gs}} = 2.33811 \left(mg^2\hbar^2/2\right)^{1/3}.

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