{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

# hw2aa - PHYS 507 Homework II Assigned Wednesday Due Friday...

This preview shows pages 1–2. Sign up to view the full content.

PHYS 507 Homework II Assigned: October 15, 2003, Wednesday. Due: October 24, 2003, Friday, at 5:00 pm. 1. Let T ( a ) be the translation operator corresponding to displacement a . (a) Calculate T ( a ) | p 0 i where | p 0 i is a momentum eigenket. (b) Let | φ i be the state obtained by translating the state | ψ i by a distance a , i.e., | φ i = T ( a ) | ψ i . What is the relationship between the momentum-space wavefunctions of these kets. (Relate ˜ φ ( p 0 ) to ˜ ψ ( p 0 )). 2. Let A = ( xp + px ) / 2. Define the operator S ( μ ) by S ( μ ) = exp - i ¯ h μA . (a) Re-express S ( μ 1 ) S ( μ 2 ) and S ( μ ) in a suitable form. Is S ( μ ) unitary? (b) Calculate i ¯ h [ A, x ] and i ¯ h [ A, p ]. (c) Calculate S ( μ ) xS ( μ ) and S ( μ ) pS ( μ ) . (d) Let | φ i = S ( μ ) | ψ i . Express the expectation values of the position and momentum in the state | φ i in terms of expectation values in | ψ i . (i.e., what is h x i φ = h φ | x | φ i in terms of h x i ψ and what is h p i φ in terms of h p i ψ ?) 3. Let the position-space wavefunction for a ket | ψ i be ψ ( x 0 ) = h x 0 | ψ i = Ne ikx 0 for 0 < x < a , 0 otherwise .

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.
• Spring '11
• starg
• Complex number, Schwarz, schwarz inequality, uncertainty relation, position-space wavefunction, uncertainty relation be1

{[ snackBarMessage ]}