a) For a particle in a one-dimensional box of length L, do the energy levels move up or down if the box gets longer? Explain your answer clearly. b) Consider a particle in a two-dimensional box of side lengths a and b, where b = 2a. In which direction is it more expensive (in terms of energy) to add nodes? Explain your answer clearly. c) Consider a particle in a two-dimensional box of side lengths a and b, where b = 2a. Write down the quantum numbers corresponding to the rst (lowest) 5 energy levels of this system. Note any degeneracies.
a) For a particle in a one-dimensional box of length L, do the energy levels move up or down if the box gets longer? Explain your answer clearly. b) Consider a particle in a two-dimensional box of side lengths a and b, where b = 2a. In which direction is it more expensive (in terms of energy) to add nodes? Explain your answer clearly. c) Consider a particle in a two-dimensional box of side lengths a and b, where b = 2a. Write down the quantum numbers corresponding to the rst (lowest) 5 energy levels of this system. Note any degeneracies.
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a) For a particle in a one-dimensional box of length L, do the energy levels move up or
down if the box gets longer? Explain your answer clearly.
b) Consider a particle in a two-dimensional box of side lengths a and b, where b = 2a.
In which direction is it more expensive (in terms of energy) to add nodes? Explain your
answer clearly.
c) Consider a particle in a two-dimensional box of side lengths a and b, where b = 2a.
Write down the quantum numbers corresponding to the rst (lowest) 5 energy levels of this
system. Note any degeneracies.
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