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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.)

University Physics Volume 3
University Physics Volume 3
17th Edition
ISBN:9781938168185
Author:William Moebs, Jeff Sanny
Publisher:William Moebs, Jeff Sanny
Chapter7: Quantum Mechanics
Section: Chapter Questions
Problem 7.10CYU: Check Your Understanding A proton with kinetic energy 1.00 eV is incident on a square potential...
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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.)
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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