Problem 2.11 (a) Compute (x). (p). (x2), and (p²), for the states o (Equation 2.60) and ₁ (Equation 2.63), by explicit integration. Comment: In this and other problems involving the harmonic oscillator it simplifies matters if you introduce the variable = √/mw/h.x and the constant a = (mco/xh)¹/4 (b) Check the uncertainty principle for these states. (c) Compute (7) and (V) for these states. (No new integration allowed!) Is their sum what you would expect?
Problem 2.11 (a) Compute (x). (p). (x2), and (p²), for the states o (Equation 2.60) and ₁ (Equation 2.63), by explicit integration. Comment: In this and other problems involving the harmonic oscillator it simplifies matters if you introduce the variable = √/mw/h.x and the constant a = (mco/xh)¹/4 (b) Check the uncertainty principle for these states. (c) Compute (7) and (V) for these states. (No new integration allowed!) Is their sum what you would expect?
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Transcribed Image Text:Problem 2.11
(a) Compute (x). (p). (x²), and (p²), for the states yo (Equation 2.60) and 1 (Equation
2.63), by explicit integration. Comment: In this and other problems involving the
harmonic oscillator it simplifies matters if you introduce the variable = √mo/hx
and the constanta (m/h)¹/4
(b) Check the uncertainty principle for these states.
(c) Compute (T) and (V) for these states. (No new integration allowed!) Is their sum
what you would expect?
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