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Chapter 2 The Schrodinger Equation

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Page 1: Chapter 2 The Schrodinger Equation.  wave function of a free particle.  Time dependent Schrodinger equation.  The probability density.  Expectation

Chapter 2

The Schrodinger Equation

Page 2: Chapter 2 The Schrodinger Equation.  wave function of a free particle.  Time dependent Schrodinger equation.  The probability density.  Expectation

2

wave function of a free particle.Time dependent Schrodinger equation.The probability density. Expectation values for momentum and

energy.Operators. Relation between expectation values and operators.

Page 3: Chapter 2 The Schrodinger Equation.  wave function of a free particle.  Time dependent Schrodinger equation.  The probability density.  Expectation

3

Wave equation

Dr. Maha Torjman

Page 4: Chapter 2 The Schrodinger Equation.  wave function of a free particle.  Time dependent Schrodinger equation.  The probability density.  Expectation

4

Classical Wave equation

Dr. Maha Torjman

Page 5: Chapter 2 The Schrodinger Equation.  wave function of a free particle.  Time dependent Schrodinger equation.  The probability density.  Expectation

Schrödinger Wave equation

Dr. Maha Torjman5

Page 6: Chapter 2 The Schrodinger Equation.  wave function of a free particle.  Time dependent Schrodinger equation.  The probability density.  Expectation

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Page 7: Chapter 2 The Schrodinger Equation.  wave function of a free particle.  Time dependent Schrodinger equation.  The probability density.  Expectation

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wave function for a free particle.

Dr. Maha Torjman

E0 = 0 from the relativistic ParticleE0 = 0 from the relativistic Particle

Page 8: Chapter 2 The Schrodinger Equation.  wave function of a free particle.  Time dependent Schrodinger equation.  The probability density.  Expectation

8

wave function for a free particle

Dr. Maha Torjman

Page 9: Chapter 2 The Schrodinger Equation.  wave function of a free particle.  Time dependent Schrodinger equation.  The probability density.  Expectation

9Dr. Maha Torjman

Page 10: Chapter 2 The Schrodinger Equation.  wave function of a free particle.  Time dependent Schrodinger equation.  The probability density.  Expectation

10Dr. Maha Torjman

Page 11: Chapter 2 The Schrodinger Equation.  wave function of a free particle.  Time dependent Schrodinger equation.  The probability density.  Expectation

11Dr. Maha Torjman

Page 12: Chapter 2 The Schrodinger Equation.  wave function of a free particle.  Time dependent Schrodinger equation.  The probability density.  Expectation

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Page 13: Chapter 2 The Schrodinger Equation.  wave function of a free particle.  Time dependent Schrodinger equation.  The probability density.  Expectation

13

Dr. Maha Torjman

Page 14: Chapter 2 The Schrodinger Equation.  wave function of a free particle.  Time dependent Schrodinger equation.  The probability density.  Expectation

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Momentum and Energy operators

Dr. Maha Torjman

Page 15: Chapter 2 The Schrodinger Equation.  wave function of a free particle.  Time dependent Schrodinger equation.  The probability density.  Expectation

15Dr. Maha Torjman

Page 16: Chapter 2 The Schrodinger Equation.  wave function of a free particle.  Time dependent Schrodinger equation.  The probability density.  Expectation

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( Example using operators )

Page 17: Chapter 2 The Schrodinger Equation.  wave function of a free particle.  Time dependent Schrodinger equation.  The probability density.  Expectation

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Dr. Maha Torjman

Page 18: Chapter 2 The Schrodinger Equation.  wave function of a free particle.  Time dependent Schrodinger equation.  The probability density.  Expectation

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Page 19: Chapter 2 The Schrodinger Equation.  wave function of a free particle.  Time dependent Schrodinger equation.  The probability density.  Expectation

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Expectation Value

Page 20: Chapter 2 The Schrodinger Equation.  wave function of a free particle.  Time dependent Schrodinger equation.  The probability density.  Expectation

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Page 21: Chapter 2 The Schrodinger Equation.  wave function of a free particle.  Time dependent Schrodinger equation.  The probability density.  Expectation

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Page 22: Chapter 2 The Schrodinger Equation.  wave function of a free particle.  Time dependent Schrodinger equation.  The probability density.  Expectation

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Page 23: Chapter 2 The Schrodinger Equation.  wave function of a free particle.  Time dependent Schrodinger equation.  The probability density.  Expectation

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Dr. Maha Torjman

Page 24: Chapter 2 The Schrodinger Equation.  wave function of a free particle.  Time dependent Schrodinger equation.  The probability density.  Expectation

24

Page 25: Chapter 2 The Schrodinger Equation.  wave function of a free particle.  Time dependent Schrodinger equation.  The probability density.  Expectation

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Page 26: Chapter 2 The Schrodinger Equation.  wave function of a free particle.  Time dependent Schrodinger equation.  The probability density.  Expectation

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Page 27: Chapter 2 The Schrodinger Equation.  wave function of a free particle.  Time dependent Schrodinger equation.  The probability density.  Expectation

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Page 28: Chapter 2 The Schrodinger Equation.  wave function of a free particle.  Time dependent Schrodinger equation.  The probability density.  Expectation

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Expectation Values

Dr. Maha Torjman

Page 29: Chapter 2 The Schrodinger Equation.  wave function of a free particle.  Time dependent Schrodinger equation.  The probability density.  Expectation

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Dr. Maha Torjman

Page 30: Chapter 2 The Schrodinger Equation.  wave function of a free particle.  Time dependent Schrodinger equation.  The probability density.  Expectation

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Dr. Maha Torjman

Page 31: Chapter 2 The Schrodinger Equation.  wave function of a free particle.  Time dependent Schrodinger equation.  The probability density.  Expectation

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Page 32: Chapter 2 The Schrodinger Equation.  wave function of a free particle.  Time dependent Schrodinger equation.  The probability density.  Expectation

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Dr. Maha Torjman

Page 33: Chapter 2 The Schrodinger Equation.  wave function of a free particle.  Time dependent Schrodinger equation.  The probability density.  Expectation

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Expectation value and operators

Dr. Maha Torjman

Page 34: Chapter 2 The Schrodinger Equation.  wave function of a free particle.  Time dependent Schrodinger equation.  The probability density.  Expectation

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Dr. Maha Torjman

Page 35: Chapter 2 The Schrodinger Equation.  wave function of a free particle.  Time dependent Schrodinger equation.  The probability density.  Expectation

35Dr. Maha Torjman

Page 36: Chapter 2 The Schrodinger Equation.  wave function of a free particle.  Time dependent Schrodinger equation.  The probability density.  Expectation

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Time-independent Schrodinger equation(1)

Dr. Maha Torjman

Page 37: Chapter 2 The Schrodinger Equation.  wave function of a free particle.  Time dependent Schrodinger equation.  The probability density.  Expectation

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Time-independent Schrodinger equation(2)

Dr. Maha Torjman

Page 38: Chapter 2 The Schrodinger Equation.  wave function of a free particle.  Time dependent Schrodinger equation.  The probability density.  Expectation

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Time-independent Schrodinger equation(3)

Dr. Maha Torjman

Page 39: Chapter 2 The Schrodinger Equation.  wave function of a free particle.  Time dependent Schrodinger equation.  The probability density.  Expectation

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Time-independent Schrodinger equation(4)

Page 40: Chapter 2 The Schrodinger Equation.  wave function of a free particle.  Time dependent Schrodinger equation.  The probability density.  Expectation

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Required properties of eigenfunctions

Dr. Maha Torjman

Page 41: Chapter 2 The Schrodinger Equation.  wave function of a free particle.  Time dependent Schrodinger equation.  The probability density.  Expectation

41

Dr. Maha Torjman

Page 42: Chapter 2 The Schrodinger Equation.  wave function of a free particle.  Time dependent Schrodinger equation.  The probability density.  Expectation

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Page 43: Chapter 2 The Schrodinger Equation.  wave function of a free particle.  Time dependent Schrodinger equation.  The probability density.  Expectation

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Dr. Maha Torjman

Page 44: Chapter 2 The Schrodinger Equation.  wave function of a free particle.  Time dependent Schrodinger equation.  The probability density.  Expectation

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Example ( standard deviation )

Page 45: Chapter 2 The Schrodinger Equation.  wave function of a free particle.  Time dependent Schrodinger equation.  The probability density.  Expectation

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Dr. Maha Torjman

Page 46: Chapter 2 The Schrodinger Equation.  wave function of a free particle.  Time dependent Schrodinger equation.  The probability density.  Expectation

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Summary(2)

Dr. Maha Torjman

Page 47: Chapter 2 The Schrodinger Equation.  wave function of a free particle.  Time dependent Schrodinger equation.  The probability density.  Expectation

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Homework