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In quiz last week you considered a system described by a wave function of the form P(x) = N a (x-a) for o

In quiz last week you considered a system described by a wave function of the form P(x) = N a (x-a) for o

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In quiz last week you considered a system described by a wave function of the form P(x) = N a (x-a) for o <xsa and p(x) = o otherwise. In particular in problem (2) of Quiz 1 you found that the normalization constant N had the value N = 30/2/a5/2. What is the value of the expectation value of the position of a particle <8> = dx $(x)* & ¢(x) in a system described by the wave function p(x)? O a (8) =5/a? Ob. (8) = x²/5 O C. * (8) = (a + x)/2 Od () = a/2 Oe. ° <8)= a²/4
Transcribed Image Text:In quiz last week you considered a system described by a wave function of the form P(x) = N a (x-a) for o <xsa and p(x) = o otherwise. In particular in problem (2) of Quiz 1 you found that the normalization constant N had the value N = 30/2/a5/2. What is the value of the expectation value of the position of a particle <8> = dx $(x)* & ¢(x) in a system described by the wave function p(x)? O a (8) =5/a? Ob. (8) = x²/5 O C. * (8) = (a + x)/2 Od () = a/2 Oe. ° <8)= a²/4
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The wave function is given byϕ(x)=N a(x-a)  for 0≤x≤a        =0x^=∫-∞+∞ dx ϕ*(x) x^ ϕ(x)       =∫-∞00 dx+∫0aNa(x-a)2x dx+∫a∞0 dx       =N2a2∫0ax-a2x dx       =N2 a2∫0ax2+a2-2ax x dx      =N2 a2 ∫0a (x3 dx+a2x dx-2ax2 dx)     =N2a2x44+a2x22-2ax33

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