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jtbell

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why do we normalise

If the wave function ψ is normalized, then we can calculate the probability that the particle lies between x=a and x=b (in the one-dimensional case) simply by evaluating the integral $$P(a \leq x \leq b) = \int^b_a {\psi^*\psi dx}$$

and how do we normalise

An un-normalized ψ has an arbitrary constant overall multiplicative factor, call it A. For example, we might have $$\psi(x) = Ae^{-x^2}$$ To normalize ψ, we find the value of A that makes this equation true: $$\int^{+\infty}_{-\infty} {\psi^*\psi dx} = 1$$ That is, we evaluate the integral, whose result must include a factor of A

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cgk

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As long as you always evaluate expectation values as [tex]\langle A\rangle = \frac{\langle \Psi|\hat A|\Psi\rangle}{\langle\Psi|\Psi|\rangle},[/tex]

then yes, that is a valid perspective---but not one shared by all instructors, so be careful in examinations. But in any case, note that the wave function property of being normalizable (not normalized)

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