A more simple question, so I am watching a quantum mechanics lecture on potentials of free particles and am doing the general solution of schrodinger's stationary equation for a free particle when I was told to normalize the solution (which I can do all well and good) but I have no idea what it actually means to "normalize" My question being what is normalization ? What does its product describe ?
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Born's rule: the probability density of finding a particle in a certain place is proportional to its square absolute value.
To change the "is proportional to" to "is", you multiply the wave function by a constant so that the absolute value squared integrates to 1, and so acts as a probability density function.
That's called normalisation, or normalising the wave function.
Andrea
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One peculiar fact about a real life wave function $\psi$ is that it can be normalized. In order to analyze and compare the various outcomes of the solution of a Schrodinger equation, one need to assign a quality that is unique to all the wave functions, that which is to transform them such that their area is always 1.
Sathyam
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