Homework5

# Homework5 - Physics 401 - Homework #5 1) A quantum...

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Physics 401 - Homework #5 1) A quantum mechanical state in two bases. A quantum mechanical particle-in-a-box is in a superposition of two stationary states, the n = 4 state and the n = 5 state. The superposition is an equal mixture of the two states, but the n = 5 state is out-of-phase by an angle of compared to the n = 4 state. We can represent this state by a ket-vector: state QM favorite our , but this symbol doesn't tell us much about the state. We can, however, write the state in other forms which are more explicit, and more useful for doing calculations. For example, we can project the state into the position basis, or we can project it into the energy basis. a) (3 points) Write down an explicit representation of this state in the position (x) basis. In other words, write down the wave function (x) for this state. b) (3 points) Write down an explicit representation for this state in the energy basis. In other words, write down the {a n } for this state in a column vector format. c) (3 points) What is the energy basis good for? To answer this, name one type of question that requires almost no calculation to answer in the energy basis. Also name a second type of question that is similarly easy to answer in the position basis. d) (3 points) Calculate the overlap between this state and the state from Homework #4, question 1, working in the energy basis. In other words, calculate state QM favorite our question Homework for state QM the 1 4 using the column-vector and row-vector format of the energy basis. You may use the

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## Homework5 - Physics 401 - Homework #5 1) A quantum...

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