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# Probability, Probability Density, and Expectation Value

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Please explain the differences (i.e. what does each measure) between:

probability

probability density

expectation value

https://brainmass.com/physics/fluid-dynamics/probability-probability-density-expectation-value-153846

#### Solution Summary

This solution explains the differences between probability, probability density and expectation value with worked examples.

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## Expectation Value, Probability Density, Eigen Function

See the attached file.

1. What is meant by an expectation value?

2. What does it mean when we say that 'mod Psi-square' is a 'probability density', as opposed to a probability?

3. What is the difference between an operator that operates on an eigen function and one that operates on any function?

4. What is meant when we say that two operators either commute or do not commute?

5. What is Quantum Mechanical Tunneling?

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