The Finite Square Well Potential, case: E ≤ V_o

In graphing the expressions for each equation, we can this famous graph in quantum mechanics showing the discrete energy values for a finite square well potential.



Note that the number of solutions depend on the size of R, which in turn depends on the depth V_o and the width a of the well.



Also, in the limiting case V_o→∞, the circle's radius R becomes infinite we recover the energy expression for the infinite well.

1. The Free Particle: Continuous States
2. The Free Particle: Analyzing the Solutions
3. The Free Particle: Are Continuous States Physical?
4. The Free Particle: A Gaussian Wave Packet
5. The Free Particle: Calculating Our Wave Packet
6. Solving the Schrödinger Equation
7. Description of Plane Waves
8. Probability Current Density
9. Calculating R and T
10. Explaining Quantum Behavior
11. Particle-like Gets Stopped
12. The Strange Evanescent Wave
13. Infinite Square Well: Deriving Discrete Energy Value
14. Infinite Square Well: What is Zero-Point Energy?
15. Infinite Square Well: Unusual Probability Densities
16. The Scattering Problem
17. Ratio Transmitted Particles
18. Energy Values and Resonance
19. Full Transmission of Part
20. Tunneling: Setting the Situation
21. Tunneling: Deciphering the Wave-like Particle
22. Tunneling: Penetrating the Potential Barrier
23. Tunneling: Further Analysis of T
24. Tunneling: The WKB Approximation Method
25. Introduction
26. Unphysical Solutions
27. Fourier Transform Revisit
28. Outside the Well
29. Anti/Symmetric Solutions
30. Boundary Conditions
31. A Graphical Solution
32. Discrete Energy Specturm

In this course, GMath Physics Instructor Donny Lee gives 32 video lessons on Quantum Mechanics and Physical Problems in One-Dimension.