Half-Harmonic Oscillator to Full-Harmonic Potential

In summary, the conversation discusses finding the allowed energies of a potential, with one person suggesting that all odd-numbered energies in the ordinary harmonic oscillator potential are allowed due to ψ(0)=0 in the corresponding wave functions. The new inquiry is about the probability of maintaining the same energy if the infinite potential is removed instantly. The person suggests that the probability shouldn't change because the odd solution is already part of the new solutions, but also considers the possibility of there being twofold more states to go to, resulting in a 0.5 probability. They are then advised to calculate the probability rather than guessing.
  • #1
Eigengore
1
0

Homework Statement


This problem was already answered:
"I have to find the allowed energies of this potential:

V(x)= (mω2^2)/2 for x>0
infinite for x<0

My suggestion is that all the odd-numbered energies (n = 1, 3, 5...) in the ordinary harmonic osc. potential are allowed since
ψ(0)=0
in the corresponding wave functions and this is consistent with the fact that
ψ(x)
has to be 0 where the potential is infinite."

now the new inquiry is that if the infinite potential is removed instantly. What is the probability of maintaining the same energy.

Homework Equations



none given aside from the other post

The Attempt at a Solution



my guess is that it shouldn't change because the odd solution is already part of the new solutions, thus it shouldn't switch. But I am tempted to consider that there are twofold more states to go to so the probability of maintaining the state is 0.5
 
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  • #2
Instead of guessing, why don't you calculate the probability?
 

FAQ: Half-Harmonic Oscillator to Full-Harmonic Potential

What is a half-harmonic oscillator?

A half-harmonic oscillator is a type of mechanical system that exhibits oscillatory behavior, where the restoring force is proportional to the displacement but only acts in one direction. This means that the system will oscillate back and forth in a linear fashion, but will only experience a force in one direction.

What is a full-harmonic potential?

A full-harmonic potential is a mathematical function that describes the potential energy of a system, such as a half-harmonic oscillator. It is a parabolic function that increases quadratically with displacement and represents the restoring force acting on the system.

How does a half-harmonic oscillator relate to a full-harmonic potential?

A half-harmonic oscillator can be thought of as a simplified version of a full-harmonic potential, where the system only experiences a restoring force in one direction. This can be mathematically represented by taking the absolute value of the full-harmonic potential function, effectively cutting it in half.

What are the applications of a half-harmonic oscillator to full-harmonic potential?

The half-harmonic oscillator to full-harmonic potential model has many applications in physics, including studying the behavior of mechanical systems, analyzing the motion of particles in a potential field, and understanding the properties of materials such as crystals. It is also used in various engineering fields, such as in the design of mechanical systems and structures.

How is the behavior of a half-harmonic oscillator to full-harmonic potential different from a full-harmonic oscillator?

The main difference between a half-harmonic oscillator to full-harmonic potential and a full-harmonic oscillator is the directionality of the restoring force. In a full-harmonic oscillator, the force is proportional to the displacement in both directions, while in a half-harmonic oscillator, it is only present in one direction. This results in different types of oscillatory behavior for the two systems.

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