Chapter 2

The Schrodinger Equation

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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.

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Wave equation

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Classical Wave equation

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Schrödinger Wave equation

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wave function for a free particle.

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

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wave function for a free particle

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Momentum and Energy operators

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( Example using operators )

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Expectation Value

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Expectation Values

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Expectation value and operators

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Time-independent Schrodinger equation(1)

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Time-independent Schrodinger equation(2)

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Time-independent Schrodinger equation(3)

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Time-independent Schrodinger equation(4)

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Required properties of eigenfunctions

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Example ( standard deviation )

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Summary(2)

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Homework