Suppose a quanton's wavefunction at a given time is y(x) = Asin(2πx/L) for - L≤ x L and y(x) = 0 everywhere else, where A is a scaling constant and L is a constant with untis of length. Suppose also the energy eigenfunction associated with the energy eigenvalue E is VE(x) = Bcos(лx/L) for - L≤x≤ ½ L and y(x) = 0 everywhere else, where B is a scaling constant. What is the probability that if we determine the quanton's energy, we get the result E? (Hint: Do not do an integral. Draw graphs of these functions and think about what the product of these function should look at. Recall that a function's integral delivers the area under that function's curve.)
Suppose a quanton's wavefunction at a given time is y(x) = Asin(2πx/L) for - L≤ x L and y(x) = 0 everywhere else, where A is a scaling constant and L is a constant with untis of length. Suppose also the energy eigenfunction associated with the energy eigenvalue E is VE(x) = Bcos(лx/L) for - L≤x≤ ½ L and y(x) = 0 everywhere else, where B is a scaling constant. What is the probability that if we determine the quanton's energy, we get the result E? (Hint: Do not do an integral. Draw graphs of these functions and think about what the product of these function should look at. Recall that a function's integral delivers the area under that function's curve.)
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Chapter7: Quantum Mechanics
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Transcribed Image Text:Suppose a quanton's wavefunction at a given time is y(x) = Asin(2πx/L) for - L≤
x L and y(x) = 0 everywhere else, where A is a scaling constant and L is a constant
with untis of length. Suppose also the energy eigenfunction associated with the energy
eigenvalue E is VE(x) = Bcos(лx/L) for - L≤x≤ ½ L and y(x) = 0 everywhere else,
where B is a scaling constant. What is the probability that if we determine the quanton's
energy, we get the result E? (Hint: Do not do an integral. Draw graphs of these functions
and think about what the product of these function should look at. Recall that a function's
integral delivers the area under that function's curve.)
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