- #1
nonequilibrium
- 1,439
- 2
Given the basic result that the harmonic potential well has the energy levels it has, are there ways to convincingly deduce the qualitative properties of the energy levels given a certain potential well?
Take for example a Morse potential, is there a way to deduce (vague if need be, exact if possible) that there will be an infinite amount of energy levels inside the well and that they monotonically get closer to each other? (without solving the Schrödinger equation)
As a side question, are there convincing arguments to qualitatively describe the shape of a free wave packet as it crosses a local potential? For example, if a free quantum wave approaches from the left across a potential initally constant but beginning to drop, will the amplitude decrease, increase or stay the same?
Take for example a Morse potential, is there a way to deduce (vague if need be, exact if possible) that there will be an infinite amount of energy levels inside the well and that they monotonically get closer to each other? (without solving the Schrödinger equation)
As a side question, are there convincing arguments to qualitatively describe the shape of a free wave packet as it crosses a local potential? For example, if a free quantum wave approaches from the left across a potential initally constant but beginning to drop, will the amplitude decrease, increase or stay the same?