Show that, for general operators A and B that have a commutation |, B| = C,...
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Show that, for general operators A and B that have a commutation |Â, B| = CÂ, "/ relation of the form one has ƒ (B) = f(B+c1)  for an arbitrary function f. Hint: You can Taylor-expand the function. (b) (1 point) Apply this result to the harmonic-oscillator ladder operators â and at and the number operator = â¹â and show that î â e¹ = eâ, e-n at en e-^ât. e -Xn = (c) (2 points) Show that for a Hermitian operator, the eigenvectors corresponding to different eigenvalues are orthogonal. 1 Show that, for general operators A and B that have a commutation |Â, B| = CÂ, "/ relation of the form one has ƒ (B) = f(B+c1)  for an arbitrary function f. Hint: You can Taylor-expand the function. (b) (1 point) Apply this result to the harmonic-oscillator ladder operators â and at and the number operator = â¹â and show that î â e¹ = eâ, e-n at en e-^ât. e -Xn = (c) (2 points) Show that for a Hermitian operator, the eigenvectors corresponding to different eigenvalues are orthogonal. 1
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a To show that ffc1 for an arbitrary function f we can use the commutation relation c and the Taylor expansion of fc1 Using the commutation relation w... View the full answer
Related Book For
Income Tax Fundamentals 2013
ISBN: 9781285586618
31st Edition
Authors: Gerald E. Whittenburg, Martha Altus Buller, Steven L Gill
Posted Date:
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