Question

We normally think of the one-dimentional well as being horizontal. Suppose it is vertical; then the potential energy of the particle depends on x because of the presence of the gravitational field. Calculate the first-order correction to the zero-point energy, and evaluate it for an electron in a box on the surface of the earth. Account for the result. Hint. The energy of the particle depends on its heigh as mgx where g= 9.81 ms^-2. Becuse g is so small, the energy correction is tiny; but it would be significant if the box were on the surface of a neutron star.

Answer 1

Solunane ame dimentian well IL VAD = mg 20x co tozzo a mgz zlo forem schrodingen Equaticom 4020 4 col=0 - zm cf? YLE) + mg z Plz) = EU2 dza dépez) - 2m (mg 2 - ) WCZ) = 0 est *= (in mo mag 2-E) 1n 0400-) = 0 The Standard differential @queettom $() = Bai 6) A16 = #S"com () at Aim) is called Asiry funchian. En = + (1 mg-47% en 63 = 2.330 (gemy? Es' z 2-33 8 x(ị mg 2 #2 743 E = +2 ama? Eloral for Ground state ET = 772 72 2 + 2mg

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