May 5, 2020
Quantum Bound States
65.02fs
Learning Goals
Visualize wave functions, probability densities, and energy levels for bound states in various
potentials.
Describe how multiple representations used for wave functions relate to one another.
Explain what is and is not time-dependent for an energy eigen-state and a superposition
state.
Predict how the curvature and amplitude of the wave function and the spacing of the
energy levels depends on the shape of the potential and the mass of the particle.
General remarks about the simulation
The simulation solves the 1D Schrodinger equation numerically in real time.
The mass is set to the electron mass.
The wave functions are not normalized.
There is no option for an infinite square well potential, but you can approximate it by
making the height of the finite well very large.
Purpose: The purpose of this experiment was to demonstrate the difference aspects of
"Quantum Bound States" such as: probability densities, wave functions, and energy
levels. In this experiment, three different potential wells were being experienced such as
square well ,asymmetric potential well, and other potential wells.
1. Square well (using One Well option)
a. You'll notice that you can't adjust the total energy in this exercise. Why not?
Answer:
This exercise is designed for Quantum Bound States, and the criteria for this is that the
energy should be smaller than potentials
b. Describe the stationary-state wave function W for different eigen-states and explain
the variations in W with total energy.
Answer:
W is called stationary states which are the states of definite energy.
nIX sin n=1,2,3
nx)
n2* h 2 We know that En = n2 * 2T2 , n = 1,2,3,... and E1 and 1 are called ground 2m L2
energy state.
XIU -iEnt/hsin ,n = 1,2,3... L
W(x,t)=Y(x)e(-iEth)-n(x,t)=
The number of peaks on the graph is equal to n value.
12
(a)
1212
(b)
20
(c)
c. Vary the potential depth. Describe the change in W and the probability density I *W.
Explain the variations.
Answer: