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Home Answered Questions Advanced Physics The Wave Functions For The Energy Eigenstates For The Particle In An Infinite Well Of Width L Is Cen

(Solved): The Wave Functions For The Energy Eigenstates For The Particle In An Infinite Well Of Width L Is Cen ...

The wave functions for the energy eigenstates for the particle in an infinite well of width L is centered at L/2 and the corresponding energies are:

\Psi_n (x) = \sqrt\frac{2}{L} cos\frac{n \pi x}{L} , n \enskip odd \\ \Psi_n (x) = \sqrt\frac{2}{L} sin\frac{n \pi x}{L} , n \enskip even \\ E_n =\frac{n^2 \pi^2 \hbar^2}{2mL^2}

The wave function of particle in infinite square well is:\Psi(x) = \frac{1}{\sqrt(5)}[2\psi_1(x) +i\psi_2(x)]

1.You make a measurement of the energy of the particle. What are the possible results and what are the corresponding probabilities?

2.If the results of energy measurement is the largest possible value, what is the wave function for the state after the measurement?

3.After measuring the energy of the particle you measure position. What is the most probable result of this measurement?

4. Does your answer to 3 depend on how much time has passed between energy and position measurement?

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