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Lesson: The Schrödinger Equation

Worksheet • 13 Questions

Q1:

In the solution of the SchrΓΆdinger equation for the rigid rotor system, what is the degeneracy of an energy level with angular momentum quantum number ?

Q2:

The SchrΓΆdinger equation for the rigid rotor system must be solved with the spherical coordinate system. What is the correct expression for calculating the average value of 𝐿 π‘₯ , the π‘₯ component of the angular momentum?

  • A ⟨ 𝐿 ⟩ = ο„Έ ο„Έ π‘Œ ( πœƒ , πœ™ ) Μ‚ 𝐿 π‘Œ ( πœƒ , πœ™ ) πœƒ πœ™ π‘₯ πœ‹ 0 2 πœ‹ 0 1 2 βˆ— π‘₯ 1 2 d d
  • B ⟨ 𝐿 ⟩ = ο„Έ ο„Έ π‘Œ ( πœƒ , πœ™ ) Μ‚ 𝐿 π‘Œ ( πœƒ , πœ™ ) πœƒ πœ™ π‘₯ πœ‹ 0 ∞ βˆ’ ∞ 1 2 βˆ— π‘₯ 1 2 d d
  • C ⟨ 𝐿 ⟩ = ο„Έ ο„Έ π‘Œ ( πœƒ , πœ™ ) Μ‚ 𝐿 π‘Œ ( πœƒ , πœ™ ) πœƒ πœ™ π‘₯ ∞ 0 ∞ 0 1 2 βˆ— π‘₯ 1 2 d d
  • D ⟨ 𝐿 ⟩ = ο„Έ ο„Έ π‘Œ ( πœƒ , πœ™ ) π‘Œ ( πœƒ , πœ™ ) πœƒ πœ™ π‘₯ πœ‹ 0 2 πœ‹ 0 1 2 βˆ— 1 2 d d

Q3:

The kinetic energy operator for a one-dimensional system is:

  • A Μ‚ 𝑇 = βˆ’ ℏ 2 π‘š π‘₯ 2 2 2 d d
  • B Μ‚ 𝑇 = ℏ 2 π‘š π‘₯ 2 2 2 d d
  • C Μ‚ 𝑇 = βˆ’ 𝑖 ℏ π‘₯ d d
  • D Μ‚ 𝑇 = βˆ’ 𝑖 ℏ π‘₯ 2 2 2 d d
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