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Suppose a quanton's wavefunction at a given time is y(x) = Asin(2x/L) for – 2L ≤ 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 eigen- value E is YE (x) = Bcos(x/L) for – ¹/L ≤ x ≤ /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(2x/L) for – 2L ≤ 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 eigen- value E is YE (x) = Bcos(x/L) for – ¹/L ≤ x ≤ /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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Suppose a quanton's wavefunction at a given time is y(x) = Asin(2πx/L) for −1⁄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 eigen- value E is ye(x) = Bcos(x/L) for – ½L ≤ 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.)
Transcribed Image Text:Suppose a quanton's wavefunction at a given time is y(x) = Asin(2πx/L) for −1⁄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 eigen- value E is ye(x) = Bcos(x/L) for – ½L ≤ 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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