How to find the ground state of He atom

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SUMMARY

The discussion focuses on calculating the ground state of the helium atom using perturbation theory. The user successfully computes the first-order correction to the ground state energy but struggles with deriving the wave function due to complex integrals involving spherical harmonics and Laguerre polynomials. References to Griffiths' textbook and Schiff's "Quantum Mechanics" are highlighted as essential resources for tackling these calculations.

PREREQUISITES
  • Understanding of perturbation theory in quantum mechanics
  • Familiarity with spherical harmonics and Laguerre polynomials
  • Knowledge of quantum mechanics principles as outlined in Griffiths' textbook
  • Basic skills in integral calculus related to quantum wave functions
NEXT STEPS
  • Study perturbation theory applications in quantum mechanics
  • Review spherical harmonics and Laguerre polynomials in detail
  • Practice integrals involving quantum wave functions
  • Read Schiff L.I. "Quantum Mechanics" for advanced insights on wave functions
USEFUL FOR

Students and researchers in quantum mechanics, particularly those focusing on atomic physics and perturbation theory applications.

coki2000
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Hello PF members,

I am trying to solve for helium atom ground state by using perturbation theory. It is very easy to calculate the first order correction of ground state energy but I have no idea for how to find its wave function.

I have tried to use the first order correction formula for wave functions in Griffiths' book but it is very hard to take those integrals since it includes very complicated terms like spherical harmonics and Laguerre polynomials etc.

Can anyone help me please?

Thanks in advance.
 
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