The classically forbidden region

[NEWO]

The classically forbidden region!

Hi guys I am new here, i understand that you can't give me an answer at all but i am really struggling with a particular question in quantum physics.

Q) Calculate for the ground state of the hydrogen atom the probability of finding the electron in the classically forbidden region.

I know that the classically forbidden region is where the potential energy is greater than the kinetic energy, I know that in QM the probability is the square of the modulus of the wavefunction, and the potential is coulombs potential, I just cannot figure out how to work this out.

I would appreciate help in this!

ps I know the wave function

Thanks for your time

newo

 

[Physics Monkey]

Hi NEWO, you have your definitions a little bit backwards. Classically, the kinetic energy is a positive number thus the classically forbidden region is where the kinetic energy would be negative, or in other words where the potential energy is greater than the total energy. You know the potential energy as a function of r and you know the ground state energy so can you find this region?

By the way, welcome to PF and in the future you should try to post homework questions in the homework section, you'll get a quicker response.

 

[NEWO]

Thanks for your quick reply and i will bare what you said in mind.

In my interpretation of what you have said;

The expected kinetic energy is the hamiltonian minus the potential;

int(wavefunction(h(bar)^2/2m*laplcian of the wavefunction))dr = E + int(ke^2/r*square of mod(wavefunction))dr

the total ground state energy is given as -13.5eV

I know this is a little messy but can you see if i am on the right track

I realize I will have to use spherical ploar coordinates in this

Thanks alot

newo

 

[NEWO]

Hi NEWO, you have your definitions a little bit backwards. Classically, the kinetic energy is a positive number thus the classically forbidden region is where the kinetic energy would be negative, or in other words where the potential energy is greater than the total energy. You know the potential energy as a function of r and you know the ground state energy so can you find this region?
QUOTE]

I think i could find this would i need to use the hamiltonian operator? also how does finding the region leads to the probability of being in the region? do I have to put it into the wavefunction and then use the probability equation to find it?

thanks for your help

newo