- #1
weak_phys
- 8
- 3
- Homework Statement
- This is not a homework Q, only in the sense that I am revisiting my degree and wondering about this part of the problem (because it always bothered me): but for reference the leap is made in Griffiths 2.3.2 (2nd edition equation 2.7.4 and 2.7.5) and Liboff 7.20 (4th edition)
- Relevant Equations
- $$\frac{d^{2}\psi}{du^2} \simeq u^2 \psi$$
At the point where we 'guess' a solution to this 2nd order ODE that cannot be done analytically, I was wondering why Griff and others choose $$e^{-x^2 / 2}$$ rather than just $$e^{-x^2}$$ I've plotted both here and am left wondering what's so different? If we guessed instead the unpopular $$e^{-x^2}$$ surely we still have the same recursion formula and quantum number when we press on?