Problem 1: Simple Harmonic oscillator (a) Find the expectation value of kinetic energy T for the nth state of a simple harmonic oscillator. (b) Write p² in terms of a+ and a_ (c) Construct 2 from vo state. Vo is given in equation (2.60). Use a+ operators (d) Find , ,,, σx and σy for state 2 found in part (c). Check if the uncer- tainty principle works for this state.
Problem 1: Simple Harmonic oscillator (a) Find the expectation value of kinetic energy T for the nth state of a simple harmonic oscillator. (b) Write p² in terms of a+ and a_ (c) Construct 2 from vo state. Vo is given in equation (2.60). Use a+ operators (d) Find , ,,, σx and σy for state 2 found in part (c). Check if the uncer- tainty principle works for this state.
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Transcribed Image Text:Problem 1:
Simple Harmonic oscillator
(a) Find the expectation value of kinetic energy T for the nth state of a simple harmonic oscillator.
(b) Write p² in terms of a+ and a_
(c) Construct 2 from o state. Vo is given in equation (2.60). Use a+ operators
(d) Find < x >,< x² >,<p>,<p² >, σx and σy for state 2 found in part (c). Check if the uncer-
tainty principle works for this state.
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Step 1: To Calculate:
VIEWStep 2: Solving part (a) i.e expectation value of kinetic energy for nth state of SHO
VIEWStep 3: Solving part (b) & (c) in this step
VIEWStep 4: In this step I have calculated expectation value of x, p^2 & x^2
VIEWStep 5: Here I have checked uncertainty principle is valid or not for given 2nd excited state of SHO
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