- #1

- 3

- 0

You are using an out of date browser. It may not display this or other websites correctly.

You should upgrade or use an alternative browser.

You should upgrade or use an alternative browser.

- Thread starter indeterminate
- Start date

- #1

- 3

- 0

- #2

Staff Emeritus

Science Advisor

Homework Helper

- 16,056

- 5,126

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

Last edited:

- #3

- 3

- 0

- #4

Science Advisor

- 524

- 42

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)

Share:

- Replies
- 9

- Views
- 601

- Replies
- 5

- Views
- 568

- Replies
- 8

- Views
- 1K

- Replies
- 3

- Views
- 581

- Replies
- 13

- Views
- 864

- Replies
- 1

- Views
- 1K

- Replies
- 5

- Views
- 813

- Replies
- 4

- Views
- 1K

- Replies
- 4

- Views
- 2K

- Replies
- 2

- Views
- 893