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Unformatted text preview: r = 108 cm . This instability was one of the reasons for the discovery of quantum mechanics. 2. The Pauli matrices are deﬁned by σ 1 = ± 0 1 1 0 ² , σ 2 = ±i i ² , σ 3 = ± 11 ² . Let us consider the three matrices as components of a vector ~σ . Show that a) e i ˆ n · ~σφ = cos φ + i ˆ n · ~σ sin φ , where ˆ n is a unit vector. b) ( ~a · ~σ ) ( ~ b · ~σ ) = ~a · ~ b + i~σ · ~a × ~ b , where ~a and ~ b are any two ordinary vectors. 3. The Fourier transform of a function ψ ( ~ r ) is deﬁned by the relation: φ ( ~ p ) = Z d 3 r (2 π ¯ h ) 3 / 2 ei ¯ h ~ p · ~ r ψ ( ~ r ) . Find the Fourier transforms of the two functions ψ 1 ( ~ r ) = 1  ~ r  ψ 2 ( ~ r ) = ea 2 ~ r 2 ....
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This note was uploaded on 03/27/2011 for the course PHYS 6572 at Cornell University (Engineering School).
 '08
 ELSER, V
 mechanics, Work

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