- #1
yeahhyeahyeah
- 30
- 0
I'm pretty confused by the rules regarding the total energy, the kinetic energy, and potential of a QM system.
Does the total energy have to be positive or greater than zero? And if so, why not? I don't really understand what it means to have a negative total energy of a system I guess. I know that we treat a lot of potentials as negative, like gravitational potential, but I guess I have never found complaint with it until now.
As an example, what if you had a system described by:
V = -V0 for x< -a
0 for |x|<a
V0 for x>a
What ranges can its energy exist in? And in what range does its energy have to be for the stationary states to be physically possible (this only happens when it is a bound state?)
Lastly, this is a kind of unrelated question, but say you have a wave packet whose initial state is such that [tex]\Psi[/tex](-x) = [tex]\Psi[/tex] (x)
In other words, an odd function. Now, because of its oddness, it can only be comprised of the odd (sin functions) stationary states. If I add time evolution, since the coefficients of any even states is 0, there will NEVER in time EVER be a contribution from any even states.
So basically, if the system starts out odd/even it will remain like so forever?
Does the total energy have to be positive or greater than zero? And if so, why not? I don't really understand what it means to have a negative total energy of a system I guess. I know that we treat a lot of potentials as negative, like gravitational potential, but I guess I have never found complaint with it until now.
As an example, what if you had a system described by:
V = -V0 for x< -a
0 for |x|<a
V0 for x>a
What ranges can its energy exist in? And in what range does its energy have to be for the stationary states to be physically possible (this only happens when it is a bound state?)
Lastly, this is a kind of unrelated question, but say you have a wave packet whose initial state is such that [tex]\Psi[/tex](-x) = [tex]\Psi[/tex] (x)
In other words, an odd function. Now, because of its oddness, it can only be comprised of the odd (sin functions) stationary states. If I add time evolution, since the coefficients of any even states is 0, there will NEVER in time EVER be a contribution from any even states.
So basically, if the system starts out odd/even it will remain like so forever?