HW8 - PHYS126 Fall 2011 HW#8 Due 01 April 1 Show that the...

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PHYS126 Fall 2011 HW #8 Due 01 April 1) Show that the following function of general sinusoidal wave ) cos( ) sin( ) ( kx b kx a x + = ψ is equivalent to the following expression ikx ikx Be Ae x + = ) ( ψ . Please also give expressions for A and B in terms of a and b . [Note: k is a real number. There is no restriction on a and b ] [ ikx e , ikx e , ) sin( kx , ) cos( kx and their arbitrary linear combination all are solutions to the equation ) ( ) ( 2 2 x k x dx d ψ ψ = , but only two of them are independent.] 2) Show that the following function of general sinusoidal wave ) cos( ) sin( ) ( kx b kx a x + = ψ is equivalent to the following expression } Im{ ) sin( ) (
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