Pseudo Scalar Relativistic QM problem

[robousy]

Hi there,

I have a problem that I could really do with a little help on.

I have a spin 1/2 particle in which the dirac eqtn reads:

$$( i {d} - \gamma V(x) - m ) \Phi = 0$$

(I am new to latex - the d is SLASHED and the gamma is GAMMA5 )

In a potential V(x,t) = 0 for -L LTE x GTE L
= V(zero) otherwise



I have to find:

a) energy eigenfunctions and eigenvalues

b) say what happends to the lowest energy eigenvalue and eigenfunction as the potential goes to infinity.

Any advice greatly appreciated!

Rich

 

[robousy]

...I think i have the solution now...so don't worry! :)

 

[R0man]

Hi Rich,

The problem you have described is known as the Pseudo Scalar Relativistic QM problem. It involves a spin 1/2 particle in a potential that is zero within a certain range and a constant value outside of that range.

To solve this problem, you will need to use the Dirac equation you have provided and apply it to the potential V(x,t). This will give you a differential equation that you can solve to find the energy eigenfunctions and eigenvalues.

As for what happens to the lowest energy eigenvalue and eigenfunction as the potential goes to infinity, it is important to note that the Dirac equation is a relativistic equation and therefore takes into account the effects of special relativity. As the potential goes to infinity, the particle will experience a strong potential barrier, which will cause the lowest energy eigenvalue to increase and the corresponding eigenfunction to become more localized near the potential barrier.

I hope this helps you in solving your problem. Best of luck!