1)Consider a particle that is in the second excited state of the Harmonic oscillator. (Note: for...

1)Consider a particle that is in the second excited state of the Harmonic oscillator. (Note: for this question and the following, you should rely heavily on the raising and lowering operators. Do not do integrals.)

(a) What is the expectation value of position for this particle?

(b) What is the expectation value of momentum for this particle?

(c) What is ∆x for this particle?

2) Consider a harmonic oscillator potential.

(a) If the particle is in the state |ψ1> = √ 1/ 2 (|0> + |1>), what is <x>? <x^ 2>?

(b) If the particle is in the state |ψ2> = √ 1 /2 (|0> + |2>), what is <x>? <x ^2 >?

(c) If the particle is in the state |ψ2> = √ 1/ 3 (|0> + |2> + |3>), do you expect <x> to be zero or non-zero? What about <x^ 2 >? Why?

(d) Describe a general rule of thumb to help you quickly determine which (if any) calculations for <x>, <x^2> will reduce to zero. Does this rule also work for <p> and <p^ 2 >?

Expert Solution

I will be glad to see your comment if you have any query and thumb up if you are satisfied. Thanks !

genius_generous answered 2 years ago

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