Consider the motion of a quantum particle in a potential V(x)-ax. Use the WKB approximation to determine how the energy of the bound state E, varies with n and a for large values of n.

In quantum mechanics, the motion of a particle in a potential V(x)=axV(x) = ax, where aa is a constant, can be analyzed using the WKB approximation, particularly for the case of bound states. The WKB (Wentzel–Kramers–Brillouin) approximation is a semiclassical method used to find approximate solutions to the Schrödinger equation when the potential varies slowly. It involves solving the Schrödinger equation in regions where the classical action is large.

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