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

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Presentation transcript:

Chapter 2 The Schrodinger Equation

 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. 2

Wave equation Dr. Maha Torjman 3

Classical Wave equation Dr. Maha Torjman 4

Schrödinger Wave equation Dr. Maha Torjman 5

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wave function for a free particle. Dr. Maha Torjman E 0 = 0 from the relativistic Particle 7

wave function for a free particle Dr. Maha Torjman 8

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Momentum and Energy operators Dr. Maha Torjman 14

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( Example using operators ) 16

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Expectation Value 19

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Expectation Values Dr. Maha Torjman 28

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Expectation value and operators Dr. Maha Torjman 33

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Time-independent Schrodinger equation(1) Dr. Maha Torjman 36

Time-independent Schrodinger equation(2) Dr. Maha Torjman 37

Time-independent Schrodinger equation(3) Dr. Maha Torjman 38

Time-independent Schrodinger equation(4) 39

Required properties of eigenfunctions Dr. Maha Torjman 40

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Example ( standard deviation ) 44

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Summary(2) Dr. Maha Torjman 46

Homework 47