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Worksheet: The Schrödinger Wave Equation

Q1:

A wave function is evaluated at the rectangular coordinates ( π‘₯ , 𝑦 , 𝑧 ) = ( 2 , 1 , 1 ) in arbitrary units. What are the spherical coordinates of this position?

  • A ( 6 , 5 2 , 1 5 ) ∘ ∘
  • B ο€» √ 5 , 6 2 , 2 9  ∘ ∘
  • C ο€» √ 7 , 6 9 , 2 4  ∘ ∘
  • D ο€» √ 6 , 6 6 , 2 7  ∘ ∘
  • E ο€» √ 9 , 6 2 , 1 5  ∘ ∘

Q2:

A wave function of a particle with mass π‘š is given by where 𝛼 = 1 . 0 0 Γ— 1 0 1 0 βˆ’ 1 m .

Find the probability that the particle can be found in the interval ( 0 . 0 0 ≀ π‘₯ ≀ 0 . 5 0 Γ— 1 0 ) βˆ’ 1 0 m.