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Manfra18-2011

# Manfra18-2011 - CHAPTER 6 Quantum Mechanics II 6.1 6.2 6.3...

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6.1 The Schrödinger Wave Equation 6.2 Expectation Values 6.3 Infinite Square-Well Potential 6.4 Finite Square-Well Potential 6.5 Three-Dimensional Infinite- Potential Well 6.6 Simple Harmonic Oscillator 6.7 Barriers and Tunneling CHAPTER 6 Quantum Mechanics II Erwin Schrödinger (1887-1961) Problem set 7, due March 14th : Chapter 6: 5, 8, 10, 12, 15, 22, 23, 30, 31, 33 Keep reading carefully Chapter 6: there is a lot of important information in here.

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6.3: Infinite Square-Well Potential The simplest such system is that of a particle trapped in a box with infinitely hard walls that the particle cannot penetrate. This potential is called an infinite square well and is given by: Clearly the wave function must be zero where the potential is infinite. Where the potential is zero (inside the box), the time-independent Schrödinger wave equation becomes: The general solution is: x 0 L wher e The energy is entirely kinetic and so is positive.
Boundary conditions of the potential dictate that the wave function must be zero at x = 0 and x = L . This yields valid solutions for integer values of n such that kL = n π .

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