Potential step with E = V0; classically forbidden or allowed?

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In summary, the conversation discusses solving the time-independent Schrodinger equation for a constant potential and energy. This leads to an ordinary differential equation with a solution of y=Ax+b. The focus is on defining interval 2 as either classically allowed or classically forbidden and using this to determine the probability current densities and reflection/transmission percentages.
  • #1
hnicholls
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In describing a potential step where E = V0, with an interval 1 defined as x < 0 before the step and an interval 2 as x > 0 after the step, is the wave function in interval 2 classically allowed or classically forbidden, i.e. is it an oscillating function or a decaying exponential function?
 
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  • #2
Try solving the time-independent Schrodinger equation for the constant potential V(x)=V0 with E=V0. What do you get?
 
  • #3
you get the ordinary differential equation

d^2/dx^2(y)=0

with solution

y=Ax+b

But, what I am interested in is solving this problem by defining the wave functions in the given intervals as either classically forbidden or classically allowed and then from those values determining the probability current densities for each interval and then the reflection and transmission percentages.

But to do this, I need to determine how to define interval 2 as CA or CF.
 

Related to Potential step with E = V0; classically forbidden or allowed?

1. What is a potential step with E = V0?

A potential step with E = V0 refers to a situation in quantum mechanics where a particle encounters a sudden change in potential energy, resulting in a step-like barrier with a specific energy value (V0).

2. Is the potential step with E = V0 considered classically forbidden or allowed?

It depends on the energy of the particle. If the particle's energy is less than V0, then the potential step is considered classically forbidden, meaning that the particle does not have enough energy to overcome the barrier and will be reflected back. If the particle's energy is greater than V0, the potential step is considered classically allowed, and the particle can pass through the barrier.

3. What happens to the particle at a potential step with E = V0?

If the particle's energy is less than V0, it will be reflected back and not pass through the barrier. If the particle's energy is greater than V0, it will pass through the barrier and continue on its path.

4. How does quantum mechanics explain the behavior of a particle at a potential step with E = V0?

Quantum mechanics explains the behavior of a particle at a potential step by taking into account the wave-like nature of particles. The particle's wave function will experience a sudden change at the potential step, resulting in a reflection or transmission of the particle depending on its energy level.

5. What is the significance of a potential step with E = V0 in quantum mechanics?

The potential step with E = V0 is significant because it demonstrates the wave-like behavior of particles and the concept of energy quantization in quantum mechanics. It also has important applications in various fields such as electronics, nanotechnology, and quantum computing.

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