Does tunneling affect the energy of a particle in a finite box?

[houlahound]

using alpha decay as a concrete example is the energy of the alpha inside and outside the nucleus the same. it appears so from what I can see but alphas do have a range of energies usually up to between 4 - 9Mev. which is the same range as inside the nucleus.

my question really is does tunnelling for say a particle in a finite box to out of the finite box change the kinetic energy of the particle in any situation, always or never?

the formula for tunnelling probability does not supply info on the energy of the tunnelled particle ie from hyperphysics (simple solution);

how would one calculate the energy/frequency of the wave function for the tunnelled particle?

 

[mfb]

Energy is conserved, but the potential inside in general won't match the potential outside.

"The energy of the alpha nucleus inside the nucleus" is not really a well-defined concept. You can use this as heuristics, but there are not physically two protons and two neutrons together bouncing around.

 

[houlahound]

thanks mfb, so if energy is conserved the particle does have the same energy on the outside implying there is no loss of energy passing through the barrier?

if as mostly does a gamma is also emitted will the gamma energy reduce the alpha particle kinetic energy?

 

[mfb]

thanks mfb, so if energy is conserved the particle does have the same energy on the outside implying there is no loss of energy passing through the barrier?

Sure.
Its kinetic energy will be different if the potential is different, the total energy is conserved.

if as mostly does a gamma is also emitted will the gamma energy reduce the alpha particle kinetic energy?

Sure. Same concept: total energy is conserved.