The potential function V(x) for this equation is V(x) = (|x|-a)^2.
The parameter a represents the distance at which the potential function reaches its minimum value. It is also known as the "well depth" of the potential.
Yes, when a = 0, the potential function reduces to V(x) = |x|^2, which is the standard harmonic oscillator potential. When a = 1, the potential becomes symmetric around the origin.
The energy levels for this potential function are equally spaced, similar to the harmonic oscillator potential. However, the energy levels converge to a finite value as the energy increases, unlike the infinite energy levels for the harmonic oscillator.
Yes, the potential function can be solved analytically using the Schrödinger equation and the method of separation of variables. The resulting solutions are known as the Hermite polynomials.