ANSWER -
For an infinite one-dimensional potential energy (PE) well of width 1 nm, the energies of the first three levels can be calculated using the Schrödinger equation for a particle in a box. The solutions of the equation give us the allowed energy levels of the particle in the well. The first three energy levels are given by the equation E_n = (h^2/8mL^2) * n^2, where h is Planck's constant, m is the mass of the particle, L is the width of the well, and n is an integer starting from 1, representing the level number.
For a finite PE well, the energy levels are different from the infinite well due to the presence of the barrier. The finite well levels will be lower than the corresponding infinite well levels. The electron penetration depth into the barrier for each of the three energy levels can be calculated using the formula for transmission probability T = (2m/h^2) * (E_incident - E_barrier)^1/2, where E_incident is the energy level of the electron and E_barrier is the height of the barrier.
In conclusion, the energy levels of a finite PE well are lower than those of an infinite well, and the penetration depth into the barrier depends on the energy level of the electron.