How to solve an anharmonic oscillator perturbation problem?

In summary, The conversation discusses a homework problem involving an anharmonic oscillator with quantum states and the determination of expressions for F1 and F. The approach involves finding the partition function and using it to obtain F, with the possibility of it being a perturbation problem. A hint is given to not consider the perturbing potential V1, but instead relate the problem to an unperturbed harmonic oscillator.
  • #1
leright
1,318
19
I have a homework problem that is kinda driving me nuts...

Consider the case of an anharmonic oscillator with microsystem quantum states given by Ej = jhf - (lambda)(jhf)^2.

Using the known harmonic expressions as a starting point, determine the corresponding expression for F1 and for F, which is about equal to Fo + (lambda)F1.

Can someone give me a hint on how to approach this problem? I figure I could find the partition function easily enough since Zj = sum(e^(-(beta)Ej)). I can then plug in Ej into the Zj function. However, I am not sure how to determine that sum. Am I even approaching this problem in the right way?

Thanks.
 
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  • #2
IF you have the partition function, how do you get the F ?

Daniel.
 
  • #3
Hi leright,
This
looks like a perturbation problem to me. You don't need the perturbing potential V1 since you have the eigenvalue given in the form of an unperturbed part (relate that to the unperturbed H.O.) and a perturbation of strength lambda.
 

Related to How to solve an anharmonic oscillator perturbation problem?

1. What is statistical mechanics?

Statistical mechanics is a branch of physics that uses statistical methods to explain the behavior and properties of systems made up of a large number of particles. It bridges the gap between the microscopic world of individual particles and the macroscopic world of thermodynamics.

2. How is statistical mechanics different from thermodynamics?

Thermodynamics deals with the overall behavior and properties of a system in equilibrium, while statistical mechanics focuses on the behavior and properties of individual particles and how they contribute to the overall behavior of the system.

3. What is the goal of statistical mechanics?

The goal of statistical mechanics is to understand and predict the macroscopic properties of a system by studying the microscopic behavior of its constituent particles.

4. How does statistical mechanics relate to probability and randomness?

Statistical mechanics uses probability and randomness to describe the behavior of individual particles in a system. These probabilities are then used to calculate the overall behavior and properties of the system.

5. What are some applications of statistical mechanics?

Statistical mechanics is used in various fields such as thermodynamics, chemistry, and materials science to understand and predict the behavior and properties of systems. It is also used in fields like astrophysics to study the behavior of large systems such as galaxies.

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