Question

Please give a detailed explanation with a sketch if necessary.

Imagine an electron trapped in a potential well along the x axis. The well is of finite depth. You can not raise or lower the potential, but you can shrink or expand the x-dimension of the well. What is your best strategy to hold the electron as long as possible?

Answer 1

Please give a detailed explanation with a sketch if necessary. Imagine an electron trapped in a potential well along the x axis. The well is of finite depth You can not raise or lower the potential, but you can shrink or expand the x-dimension of the well. What is your best strategy to hold the electron as long as possible? Due to quantum tunnel effect, the electron as a quantum probability to surmount the Potential barrier. This probability is given by the transmission coefficient, which is given by T-e mass, E is the electron Energy, V% is the Potential barrier value (in a graph Energy E vs x position, it is the "height" of the barrier) , h is Planck-s constant and L is the width (x-dimension) of the well. where m is electron From this equation, we see that Probability of finding the electron outside the well decreases with the width of the well, if V% remains constant, then increasing L , the x-dimension of the well, the Probability of finding the electron inside the well increases and it means the electron will be held as long as possible