Explanation Given: The symmetric wave function is ψ S ( x 1 , x 2 ) = ψ n ( x 1 ) ψ n ′ ( x 2 ) + ψ n ′ ( x 1 ) ψ n ( x 2 ) . The asymmetric wave function is ψ A ( x 1 , x 2 ) = ψ n ( x 1 ) ψ n ′ ( x 2 ) − ψ n ′ ( x 1 ) ψ n ( x 2 ) . Formula used: The expression for combination of symmetric and asymmetric wave function is given by, ψ SA ( x 1 , x 2 ) = ψ n ( x 1 ) ψ n ′ ( x 2 ) ± ψ n ′ ( x 1 ) ψ n ( x 2 ) Calculation The expression for combination of symmetric and asymmetric wave function is calculated as, ψ SA ( x 1 , x 2 ) = ψ n ( x 1 ) ψ n ′ ( x 2 ) ± ψ n ′ ( x 1 ) ψ n ( x 2 ) { − ℏ 2 2 m [ ( ∂ 2 ∂ x 1 2 ) + ( ∂ 2 ∂ x 2 2 ) ] + U ( x 1 ) + U ( x 2 ) } ψ SA ( x 1 , x 2 ) = { − ℏ 2 2 m [ ( ∂ 2 ∂ x 1 2 ) + ( ∂ 2 ∂ x 2 2 ) ] + U ( x 1 ) + U ( x 2 ) } ( ψ n ( x 1 ) ψ n ′ ( x 2 ) ± ψ n ′ ( x 1 ) ψ n ( x 2 ) ) = { ψ n ′ ( x 2 ) ( − ℏ 2 2 m [ ( ∂ 2 ∂ x 1 2 ) + U ( x 1 ) ] ) ψ n ( x 1 ) + ψ n ( x 1 ) ( − ℏ 2 2 m [ ( ∂ 2 ∂ x 2 2 ) + U ( x 2 ) ] ) ψ n ′ ( x 2 ) ± ψ n ( x 2 ) ( − ℏ 2 2 m [ ( ∂ 2 ∂ x 1 2 ) + U ( x 1 ) ] ) ψ n ′ ( x 1 ) ± ψ n ′ ( x 1 ) ( − ℏ 2 2 m [ ( ∂ 2 ∂ x 1 2 ) + U ( x 1 ) ] ) ψ n ( x 2 ) }

2nd Edition

ISBN: 9780805303087

Author: Randy Harris

Publisher: Addison Wesley

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Question

Chapter 8, Problem 34E

To determine

The proof that symmetric and asymmetric combination are the solution of two particles Schrodinger equation.

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Chapter 8, Problem 33E

Chapter 8, Problem 35E

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