Animation 1: SHO + 10V_aexp(−10x²) | Animation 2: V₀x⁴  − 10V_ax²
Animation 3: −Vexp(−αx²) | Animation 4: eE

Please wait for the animation to completely load.

In this Exploration there are four spatially-varying wells to consider:

1. Double harmonic oscillator well: a harmonic oscillator with V_added = 10V_aexp(−10x²)
2. Double anharmonic oscillator well: an anharmonic oscillator, V(x) = V₀x⁴, with V_added = −10V_ax²
3. Gaussian well: V = −Vexp(−αx²)
4. Finite well with an applied electric field: V_added = eE

For each well, you may change parameters associated with the well's shape. To see the other bound states, simply click-drag in the energy level diagram on the left to select a level. The selected level will turn red. As you do so, answer the following question for each well: How does changing the variable parameter(s) change the energy eigenfunctions and the energy levels?