# The plots of wave function of harmonic oscillator

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1. Jun 21, 2017

### Tspirit

1. The problem statement, all variables and given/known data
In Griffiths' book "Introduction to Quantum Mechanics", Section 2.3, Chapter 2, the Fig. 2.7 gives the plots of the wave function ($\psi_{n}$) and its modulus of the harmonics oscillator, see the Appendix. With the order ($n$) increasing, they become both higher. However, according to the Equation [2.85], the wave function shouldn't be higher with $n$ increasing. They are just a normalizable wave function, if the baseline is greater than 1, it won't normalize. So how to understand the plots?

2. Relevant equations
$$\psi_{n}(x)=(\frac{m\omega}{\pi\hbar})^{1/4}\frac{1}{\sqrt{2^{n}n!}}H_{n}(\xi)e^{-\xi^{2}/2}$$
$$\xi\equiv x\sqrt{m\omega/\hbar}$$

3. The attempt at a solution
I doubt if it is just a demonstration of Energy level and the plots' height is not related to the wave function.

2. Jun 21, 2017

### WrongMan

first off, the graf you called the "modulus" is actually the probability distrbution.
wth that in mind, the lines "n=x" are (must be) your 0 line, they are just ploted over each other. was that your question?

E=(n+1/2)ħw so with n increasing you have more energy therefore you can "travel" further from the origin.

3. Jun 21, 2017

### Tspirit

Yes, that is. All of the functions should be around the horizontal axis.