In Section 5.5, it was shown that the infinite well energies follow simply from λ = h/p; t...

In Section 5.5, it was shown that the infinite well energies follow simply from λ = h/p; the formula for kinetic energy, p2/2m; and a famous standing-wave condition, λ = 2L/n. The arguments are perfectly valid when the potential energy is 0 (inside the well) and L is strictly constant, but they can also be useful in other cases. The length L allowed the wave should be roughly the distance between the classical turning points, where there is no kinetic energy left. Apply these arguments to the oscillator potential energy, U(x)=½kx2 Find the location ,v of the classical turning point in terms of E; use twice this distance for Li then insert this into the infinite well energy formula, so that E appears on both sides. Thus far, the procedure really only deals with kinetic energy. Assume, as is true for a classical oscillator, that there is as much potential energy, on average, as kinetic energy. What do you obtain for the quantized energies?