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[QUE/QM-13001]

Node id: 2767page

Using a suitable definition find the classical probability  that  a classical harmonic oscillator   will be found with position in the range \(x, x+dx\). Plot your answer as function of \(x\). Compare the plot of classical probability  with the probability as given by quantum mechanics for \(n^{th}\)  excited state for large \(n\).

 kapoor's picture 22-04-11 13:04:34 n

[QUE/QM-13002]

Node id: 2768page
  1. Find the energy eigen-functions for $E < V_0$. Verify that the energy eigenvalues are non-degenerate and continuous in this case.
  2. Verify that the energy eigenvalues are doubly degenerate for $E > V_0$. Find two linearly independent energy eigenfunctions $u_1$ and $u_2$ for energy $E$ such that the most general energy eigenfunctions is a linear combination of the two solutions $u_1$ and $u_2$.

 

 kapoor's picture 22-04-06 16:04:46 n
 
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