Question: Suppose an electron, constrained to move only in the vertical direction, sits on an impenetrable table in Earths gravitational field. Write down the (one dimensional)

Suppose an electron, constrained to move only in the vertical direction, sits on an impenetrable table in Earth’s gravitational field. Write down the (one dimensional) Schrödinger equation that determines its wavefunction as a function of height z. Use dimensional analysis to estimate its ground state energy up to a multiplicative factor. Estimate its average height above the table top, also up to a multiplicative factor.

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