- #1
Waxterzz
- 82
- 0
If you solve TISE with V=0, you get a plane wave.
This is not normalizable, so it's not a physically achievable state.
But a linear combination does (?) I know why it does from the mathematics, a linear combination of plane waves is normalizable, but what does it really mean? A free particle is associated to MORE than 1 plane wave??
Therefore you create a wavepacket with a spread around a center... From position to momentum, you switch with Fourier Transform etc etc
I don't really get it.
Why is it not normalizable from a "conceptual" point of view? A free particle has an infinite chance to be found anywhere? Is that the reason? If the free particle solution ( a single plane wave) isn't really meaning something, why does that form always come back (in solid state physics for example)
And how do you construct it in real life, a free particle wavepacket. In textbooks they say: you get a lot of momenta so the uncertainty in momentum becomes greater, hence position gets more defined and vice versa.
How can you give 1 particle more momenta to set its position right, and how can you make the uncertainty in position right to give it the right momentum. (In real life)
This is not normalizable, so it's not a physically achievable state.
But a linear combination does (?) I know why it does from the mathematics, a linear combination of plane waves is normalizable, but what does it really mean? A free particle is associated to MORE than 1 plane wave??
Therefore you create a wavepacket with a spread around a center... From position to momentum, you switch with Fourier Transform etc etc
I don't really get it.
Why is it not normalizable from a "conceptual" point of view? A free particle has an infinite chance to be found anywhere? Is that the reason? If the free particle solution ( a single plane wave) isn't really meaning something, why does that form always come back (in solid state physics for example)
And how do you construct it in real life, a free particle wavepacket. In textbooks they say: you get a lot of momenta so the uncertainty in momentum becomes greater, hence position gets more defined and vice versa.
How can you give 1 particle more momenta to set its position right, and how can you make the uncertainty in position right to give it the right momentum. (In real life)