Finding Ground State Wave Functions: Tips & Tricks

In summary, the conversation discusses the best method for finding the ground state wave functions for a given Hamiltonian, which resembles a harmonic oscillator. The suggestion of using a clever change of variables or a perturbation perspective is mentioned. The recommendation to search for references using specific keywords on Google Scholar is also made.
  • #1
LAHLH
409
1
Hi,

If I have the Hamiltonian: [itex] H=(1/2)p^2+(1/24)\lambda(x^2-v^2)^2[/itex] what is the best way to find the ground state wave functions [itex] \psi(x) [/itex]. I was thinking this sort of looks like the harmonic osscilator, so maybe a clever change of variables could do the trick? or some form of perturbation perspective?
 
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  • #2
LAHLH said:
Hi,

If I have the Hamiltonian: [itex] H=(1/2)p^2+(1/24)\lambda(x^2-v^2)^2[/itex] what is the best way to find the ground state wave functions [itex] \psi(x) [/itex]. I was thinking this sort of looks like the harmonic osscilator, so maybe a clever change of variables could do the trick? or some form of perturbation perspective?
Enter the key words
high order expansion anharmonic oscillator
into http://scholar.google.com to get a lot of references.
 
  • #3
A. Neumaier said:
Enter the key words
high order expansion anharmonic oscillator
into http://scholar.google.com to get a lot of references.

thanks, will check those out.
 

1. What is the ground state wave function?

The ground state wave function is the lowest energy state of a quantum mechanical system. It describes the probability of finding a particle in a particular position and is an important concept in quantum mechanics.

2. Why is finding the ground state wave function important?

Finding the ground state wave function allows us to understand the behavior and properties of a quantum mechanical system. It also allows us to make predictions about the system and its future behavior.

3. What are some tips for finding ground state wave functions?

Some tips for finding ground state wave functions include using symmetry arguments, utilizing the variational method, and using numerical techniques such as the Monte Carlo method. It is also important to understand the boundary conditions and constraints of the system.

4. What are some common tricks for finding ground state wave functions?

Some common tricks for finding ground state wave functions include using the separation of variables method, using the ladder operator technique, and using the Born-Oppenheimer approximation. These techniques can simplify the problem and make it easier to find the ground state wave function.

5. Can the ground state wave function be found exactly?

In most cases, the exact ground state wave function cannot be found analytically. However, approximations and numerical techniques can be used to find a close approximation of the ground state wave function. In some simple systems, the exact ground state wave function can be found using specific techniques.

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