Help with Linear Harmonic Oscillator Problem

In summary, the person is in a real dilemma and needs help with a problem due tomorrow. They are trying to show that in the ground state of a linear harmonic oscillator, the probability of finding it outside the classical limit is approximately 17%. They have not made any attempts at solving the problem and are struggling to understand it. They are being encouraged to show their own work and attempt the problem before seeking help. The key is to calculate how much of the quantum mechanics wave function overlaps with the classical one.
  • #1
sanjeeb
8
0
i m in a real problem and hav to give answers to the following problem tomorrow..please anyone help me..
Q: show that in ground state of linear harmonic oscillator ,the probability of finding oscillator outside the classical limit is nearly 17%?
 
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  • #2
You must show some of your own work in order for us to help you. What is the definition of the classical limit? What is the definition of the ground state?
 
  • #3
berkeman said:
You must show some of your own work in order for us to help you. What is the definition of the classical limit? What is the definition of the ground state?
well classical limit can be understood at the site http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/hosc6.html#c2
 
  • #4
yes we know, but we want to know what you know, and what you have done so far.

the thing is to calculate how much of the QM oscillators wave function overlaps the classical one.
 
  • #5
i m in quite a dilemma,,, icant make u understand
 
  • #6
sanjeeb said:
i m in quite a dilemma,,, icant make u understand
what we want to see is WHAT YOU have DONE to Solve your problem ? Have you made any attempts at it ? Could you say how to start, atleast make a guess ?
 
  • #7
no one will give u a complete solution by looking at the links u give and the question.
if u don't write what u have done so far using what formulae u will never get help.

this is the whole point
 
  • #8
i hav not tried anything out
 
  • #9
sanjeeb said:
i hav not tried anything out

You just have to calculate of much of the wave function is out of the classical boundrais and square the result.

Have you not tried anything?!
 

1. What is a linear harmonic oscillator?

A linear harmonic oscillator is a type of physical system that exhibits oscillatory motion around an equilibrium point. It is characterized by a restoring force that is directly proportional to the displacement from the equilibrium point and acts in the opposite direction of the displacement.

2. How do you solve a linear harmonic oscillator problem?

To solve a linear harmonic oscillator problem, you need to use the equation of motion, which is a second-order differential equation. This equation can be solved using various techniques, including the method of undetermined coefficients, the method of variation of parameters, or the Laplace transform method.

3. What is the role of the mass and spring constant in a linear harmonic oscillator?

The mass and spring constant both play crucial roles in determining the behavior of a linear harmonic oscillator. The mass determines the inertia of the system, while the spring constant determines the strength of the restoring force. A higher mass will result in a slower oscillation, while a higher spring constant will result in a faster oscillation.

4. How does the amplitude of a linear harmonic oscillator change with time?

The amplitude of a linear harmonic oscillator remains constant over time unless there is an external force acting on the system. In the absence of external forces, the amplitude will remain the same as the initial displacement from the equilibrium point.

5. Can a linear harmonic oscillator exhibit different types of motion?

Yes, a linear harmonic oscillator can exhibit different types of motion depending on the initial conditions and the system parameters. It can exhibit simple harmonic motion, where the displacement and velocity vary sinusoidally, or it can exhibit damped motion, where the amplitude decreases over time due to energy dissipation. It can also exhibit forced motion, where an external force is applied to the system, resulting in a steady-state oscillation.

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