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Harmonic Oscillator Dynamics: Force Direction and Wave Function Behavior

This video explores the behavior of a harmonic oscillator with a specific wave function at t=0. It investigates the force direction and predicts the wave function's evolution, along with estimating the energy changes. The discussion addresses why |Y|2 may not change with time and the impact of altering the initial wave function. Additionally, it delves into the real and imaginary parts of the wave function and explains the function's dependence on x and t.

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Harmonic Oscillator Dynamics: Force Direction and Wave Function Behavior

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  1. Harmonic Oscillator (harmosc1.mpg) The wave function at t = 0 has the form Y(x,0) = A exp[-x2/102] V(x) = ½ (x/50)2 & starting v = 0 Which direction is the force? What will the wave function do? Estimate E.

  2. Harmonic Oscillator (harmosc1.mpg)

  3. Harmonic Oscillator (harmosc1.mpg) Why doesn’t |Y|2 change with t? Does Y change with t? If used Y(x,0) = A exp[-x2/112], would |Y|2 change with t?

  4. Harmonic Oscillator (harmoscr.mpg) The wave function at t = 0 has the form Y(x,0) = A exp[-x2/102] V(x) = ½ (x/50)2 & starting v = 0 Only the real part of Y in this movie

  5. Harmonic Oscillator (harmoscr.mpg)

  6. Harmonic Oscillator (harmoscr.mpg) What is the real part of Y? The imaginary part? Why is the solution a function of x times a function of t?

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