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Energy Change of a Particle

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A particle of mass m is confined to move in a narrow, straight tube of length a which is sealed at both ends with V=0 inside the tube. Treat the tube as a one-dimensional infinite square well. The tube is placed at an angle theta relative to the surface of the earth. The particle experiences the usual gravitational potential V=mgh. Calculate the lowest-order change in the energy of the ground state due to gravitational potential.

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