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Problem/QM-06024

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If \(\psi(x,y,z)\)is the wave function of a particle in three dimension   write expression for probability that

  1. \(x\) is between \(x_1\) and \(x_2\);
  2. \(p_z\) lies between \(p_1\) and \(p_2\);
  3. Assume that \(\psi(\vec{r}) =  R(r) Y_{\ell m}(\theta,\phi)\). What is the probability that the particle will be found inside a sphere of radius \(R\)? What is the probability that the particle will be found outside the sphere of radius \(R\)?

 

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