finite potential wells Definition and Topics - 3 Discussions

The finite potential well (also known as the finite square well) is a concept from quantum mechanics. It is an extension of the infinite potential well, in which a particle is confined to a "box", but one which has finite potential "walls". Unlike the infinite potential well, there is a probability associated with the particle being found outside the box. The quantum mechanical interpretation is unlike the classical interpretation, where if the total energy of the particle is less than the potential energy barrier of the walls it cannot be found outside the box. In the quantum interpretation, there is a non-zero probability of the particle being outside the box even when the energy of the particle is less than the potential energy barrier of the walls (cf quantum tunnelling).

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1. Calculate the rate of probability density's movement?

1. Homework Statement Given the following diagram of a finite potential well, calculate the rate at which the right-going wave is bringing probability density up to the barrier. (Ignore interference with the left-going wave. ) (Hint: you can get the velocity from the energy, and the average...
2. Square well potential

Homework Statement Consider a particle in a square well potential: $$V(x) = \begin{cases} 0, & |x| \leq a \\ V_0, & |x| \geq a \end{cases}$$ We are interested in the bound states i.e. when ##E \leq V_0##. (1) Show that the even solutions have energies that satisfy the transcendental...
3. Some help with quantum mechanics?

Homework Statement Hi everyone. This is my first time on her so I hope I make what I'm looking for clear! The question in the book says, If V(x) = ∞, x<0 ; -Vo, 0 < x < a ; 0, x > a Solve the schrodinger equation for E < 0 inside and outside the well. Apply the boundary conditions at x...