Infinite potential barrier

In summary, the problem at hand is finding the wavefunction of a particle in a potential with different regions of zero and non-zero potential. The ground state energy must fall within the range of 0 to V. The wavefunction must be zero at the infinite barrier and at the border, satisfying the continuity criteria. This means that the particle has zero probability of being in the infinite region, leaving only the zero potential region for it to exist in. The transmission coefficient also decreases as the barrier height decreases, and the wavefunction must be continuous in both regions.
  • #1
nolanp2
53
0

Homework Statement



find the wavefunction of a particle in a potential
V(x)= 0, |x|< a
V, |x|< b (V>0)
(Infinity), |x|>=b

ground state energy 0<=E<=V

Homework Equations





The Attempt at a Solution


i know the wavefunction has to be equal to zero at the infinite barrier so when i use that as my boundary condition for the V potential region i just get that the particle has zero probability of being in this region at all, leaving only the zero potential region for it to lie within. but i can't understand why the infinite barrier should have this effect, if it weren't for this barrier the particle would be able to reach this higher energy region. can any1 help me with an explanation of this effect, or if it is not the case point out where I'm going wrong?
 
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  • #2
put up the transmission coefficent as a function of the barrier height, and you'll see that it goes to zero as the barrier height goes to zero.

And for the criteria that the wave function must be continous, it must be zero at the boarder and the wave function must be zero in the infinite region, since the particle can penetrate through it.
 

1. What is an infinite potential barrier?

An infinite potential barrier is a theoretical concept in physics that describes a situation where the potential energy of a particle is infinitely high at a certain point. This means that the particle cannot pass through or overcome this barrier.

2. How does an infinite potential barrier affect particles?

An infinite potential barrier acts as a barrier to the movement of particles. This means that particles cannot pass through the barrier and are confined to the region where the barrier exists.

3. What are some real-life examples of an infinite potential barrier?

One example of an infinite potential barrier is a particle trapped in a box with infinite potential walls. Another example is an electron trapped in an atom, where the electron experiences an infinite potential barrier at the nucleus.

4. What is the significance of an infinite potential barrier in quantum mechanics?

In quantum mechanics, an infinite potential barrier is used to model various physical systems, such as electron energy levels in atoms and particles confined in a potential well. It is also useful in understanding the concept of quantum tunneling.

5. Can an infinite potential barrier be overcome?

No, an infinite potential barrier cannot be overcome. This is because the potential energy at the barrier's location is infinitely high, making it impossible for particles to pass through or overcome it.

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