- #1

charanshah09

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And also the probability of finding the electron is given by the product of wave equation and conjugate of wave equation modulus. How does this work?

Any kind of help would be appreciated.

Thank you.

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- Thread starter charanshah09
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- #1

charanshah09

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And also the probability of finding the electron is given by the product of wave equation and conjugate of wave equation modulus. How does this work?

Any kind of help would be appreciated.

Thank you.

- #2

malawi_glenn

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For the second, one uses:

[tex] \int _a^b \psi ^*(x) \psi (x) dx [/tex]

To find the probablity that the particle, described by the normalised wavefunction psi, is between x = a and x = b.

- #3

jtbell

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In the potential well example we are considering the potential in the well to be zero and infinite outside the boundary, does this mean that the electron can move freely such that there is no opposition or restoring energy acting on it.

The classical analog is a particle that has zero net force acting on it inside the box, except at the walls. When it hits the walls, it rebounds perfectly elastically and instantaneously.

And also the probability of finding the electron is given by the product of wave equation and conjugate of wave equation modulus. How does this work?

Consider the wave function for the ground state of the "particle in a box" with walls at x = 0 and x = L:

[tex]\Psi(x,t) = \sqrt{\frac{2}{L}} \sin \left( \frac{\pi x}{L} \right) \exp \left( - \frac{i \pi^2 \hbar t}{2mL^2} \right)[/tex]

Then the probability distribution is

[tex]P(x,t) = \Psi^*(x,t) \Psi(x,t)[/tex]

[tex]P(x,t) = \left[ \sqrt{\frac{2}{L}} \sin \left( \frac{\pi x}{L} \right) \exp \left( + \frac{i \pi^2 \hbar t}{2mL^2} \right) \right] \left[ \sqrt{\frac{2}{L}} \sin \left( \frac{\pi x}{L} \right) \exp \left ( - \frac{i \pi^2 \hbar t}{2mL^2} \right) \right] [/tex]

[tex]P(x,t) = \frac{2}{L} \sin^2 \left( \frac{\pi x}{L} \right)[/tex]

which doesn't actually depend on t in this case, although in general P does depend on both x and t.

- #4

charanshah09

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Thank you once again for helping me.

- #5

charanshah09

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- #7

siddharth

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http://phet.colorado.edu/new/simulations/index.php?cat=Quantum_Phenomena

- #8

charanshah09

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