Does a Free Particle in Quantum Mechanics Have Constant Energy?

[xcorat]

Hi, I'm new to QM (and phy forum :D), and studyin alone..!

so, if you consider the free particle, it does not have a solution in the form of separable solutions(??). Which means that if the same experiment (independent, of course,) is carried out total energy is different each time at t = t_a (for constant a).

what does this mean? it seems to me like energy is created and destroyed. Is it so? or does it have to do som'n with uncertainness principle?

help me, thax a lot.

 

[muppet]

Hi xcorat, and welcome to PF
The schroedinger equation for a free particle DOES admit a separable solution- why do you think it doesn't? The general condition for this to be the case is that the potential term in the hamiltonian doesn't depend on time: V(x,t) =V(x). Here, V=0 ...
As for energy being created and destroyed... it's more true to say that the system doesn't have an energy- at least, not to begin with. The way it works is this: solving the Schroedinger equation for a time-independent potential gives you the "spectrum" of the hamilton- the range of possible energy eigenvalues. A completely free particle- which has never interacted with anything, ever- can theoretically attain any of these values. Then, when you measure its energy, its energy assumes a definite value, which it keeps for ever. It's not a physically realistic picture- it's just a very easy differential equation to solve. Realistic descriptions usually involve harder maths! There's been millions of discussions of the uncertainty principle on here before- search the forums, read a few, then come back if you get stuck.