Potential Function of Infinite Square Well - Help Needed!

In summary, the conversation discusses an expression for a potential function with specific values for different ranges of x. The question is whether this potential can be referred to as the infinite well potential and where it can be applied. It is determined that it is an infinite square well potential and the potential at ± 1 does not affect it. The use of TeX on the forum is also mentioned.
  • #1
donsammie
2
0
Please I'm new here, and would need your help with identifying what sort of potential function is described by the following expression:

V(x) = 0 for |x| < 1, =1 at x = \pm 1, and =\infty for |x|>1.

(Note that: \pm is plus (+) or minus (-) sign).

Could it be referred to as the infinite well potential? If not, what kind of potential can it be called, and where can it be applied.

I'm particular interested in solving the 1-D Schrodinger time-independent equation:

H_{0}f(x) + V(x)f(x)= E f(x),

where H_{0} is the usual Laplace operator

Thank you!
 
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  • #2
It is an infinite square well, and the potential at ± 1 does not matter here.

##V(x)=\infty## <- you can use TeX in this forum.
 
  • #3
Thank you mfb. How do you use TeX on the forum?
 

Related to Potential Function of Infinite Square Well - Help Needed!

1. What is the potential function of an infinite square well?

The potential function of an infinite square well is a piecewise function that is zero within the well (between the boundaries) and infinite outside of the well. This creates a potential barrier that particles must overcome to enter or exit the well.

2. How is the potential function related to the energy levels in an infinite square well?

The potential function is directly related to the energy levels in an infinite square well. The potential energy within the well is zero, which means that the total energy of a particle is equal to its kinetic energy. This results in quantized energy levels, where the energy of a particle can only take on certain discrete values.

3. How do the boundaries of an infinite square well affect the potential function?

The boundaries of an infinite square well determine the shape and behavior of the potential function. The potential function is zero within the boundaries and infinite outside of them. This creates a potential barrier that particles must overcome to enter or exit the well, leading to the quantization of energy levels.

4. How does the potential function affect the behavior of particles in an infinite square well?

The potential function plays a crucial role in determining the behavior of particles in an infinite square well. It creates a potential barrier that particles must overcome to enter or exit the well, leading to quantized energy levels. This also affects the probability of finding a particle at different positions within the well.

5. Can the potential function of an infinite square well be changed?

Yes, the potential function of an infinite square well can be changed by altering the boundaries or by adding a potential barrier within the well. This can result in different energy levels and behaviors of particles within the well. However, the potential function will always be zero within the boundaries of the well.

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