Find Energy Levels for Harmonic Oscillator w/ Stretch-Only Spring

In summary, a harmonic oscillator with a stretch-only spring is a type of physical system that exhibits harmonic motion with a spring providing the restoring force. The energy levels for this type of oscillator can be found using the equation E = (n + 1/2)hω and represent the different states the system can exist in. These levels are quantized and increase with the quantum number n, resulting in a ladder-like pattern. The energy levels can be affected by factors such as spring stiffness, attached mass, and external forces.
  • #1
catsarebad
72
0
for harmonic oscillator, V(x) = 1/2*m*w^2*x^2. here, the spring can be stretch or compress.

however, is if the spring can only stretch such that V(x) is infinity for x<0, then find energy level for this setup.

I don't understand the part about spring only being able to stretch. what does that turn equation into? i dunno, any hints?
 
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  • #2
Just truncate the left half of V(x) and instead of half a parabola there, you have a straight cliff. This sounds like a homework question by the way, and those belong in the homework forums.
 

Related to Find Energy Levels for Harmonic Oscillator w/ Stretch-Only Spring

What is a harmonic oscillator with a stretch-only spring?

A harmonic oscillator with a stretch-only spring is a type of physical system that exhibits harmonic motion, meaning it oscillates back and forth around a central equilibrium point. This type of oscillator is unique in that it only has a spring that provides a restoring force, rather than a combination of a spring and a mass or other object.

How do you find the energy levels for a harmonic oscillator with a stretch-only spring?

The energy levels for a harmonic oscillator with a stretch-only spring can be found using the equation E = (n + 1/2)hω, where E is the energy level, n is the quantum number, h is Planck's constant, and ω is the angular frequency of the oscillator. This equation is derived from the Schrödinger equation and can be used to calculate the energy levels for any quantum system.

What is the significance of the energy levels in a harmonic oscillator with a stretch-only spring?

The energy levels in a harmonic oscillator with a stretch-only spring represent the different states that the system can exist in. Each energy level corresponds to a different amount of energy that the oscillator can have, and these levels play a crucial role in determining the behavior and dynamics of the system.

How do the energy levels change in a harmonic oscillator with a stretch-only spring?

The energy levels in a harmonic oscillator with a stretch-only spring are quantized, meaning they can only take on discrete values. As the quantum number n increases, the energy levels also increase, but the difference between each level remains constant. This results in a ladder-like pattern of energy levels, with each rung representing a different state of the oscillator.

What factors can affect the energy levels in a harmonic oscillator with a stretch-only spring?

The energy levels in a harmonic oscillator with a stretch-only spring can be affected by various factors, such as the stiffness of the spring, the mass of the object attached to the spring, and external forces acting on the system. Changes in these factors can alter the energy levels and thus impact the behavior of the oscillator.

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