- #1
WWCY
- 479
- 14
Homework Statement
[/B]
1) I don't quite understand what 2.94 means on its own. It was derived from 2.93, yet it doesn't show a superposition of any sort. The author then takes 2.94, and attempts to normalise it by stating
##\int \Psi_k^* \Psi_k dx = \mid A^2 \mid\int dx = \infty ##
What would be the purpose of taking only 1 term from 2.93 and attempting to normalise it? Was this a simpler way of illustrating the un-normalizability of the wavefunction rather than attempting it with 2.93 as a whole?
2) The author then goes on to say (after the integral) "In the case of the free particle, then, the separable solutions do not represent physically realizable states. A free particle cannot exist in a stationary state (...) there is no such thing as a free particle with a definite energy".
a) What does a physically realizable state entail?
b) What led to the conclusion of "A free particle cannot exist in a stationary state / there is no such thing as a free particle with a definite energy"?
c) Also, what does "not having definite energy" mean? Does it mean that measurements on free particles will see variance in the energy levels observed (unlike that of stationary states)?
3) The author then formulates a general solution to the time-dependent Schrodinger equation by integrating over k:
##\Psi(x,t) = \frac{1}{\sqrt{2\pi}}\phi (k) e^{i(kx - \frac{\hbar k^2}{2m}) t} ##
and stating that this was a normalizable solution.
a) Does this mean that though a free particle can't exist as a stationary state, it can exist as a wave-packet?
Also, what are the fundamental physical differences between the two?
Thanks very, very much in advance!
P.S: I am learning QM on my own for now, and the exposure I have to QM is limited to the first 2 chapters of Griffith's book. Explanations that are not too technical would be greatly appreciated!