Manybody trial wave functions for atomic systems

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Many-body trial wave functions for atomic systems

• Rajendra Adhikari
• University of Arkansas
• Department of Physics
• 03/14/2008

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Outline

• Introduction
• Trial wave function
• Method of variation
• Many body system

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Subject entry

• It is always not possible to calculate the exact
  ground state eigenfunction of the Hamiltonian.
• Only for a few problems we can do this
• Exmaples
• Hydrogen atom, Harmonic Oscillator, One
  dimensional infinite square well

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• One of the way to get approximate solution for a
  ground state is method of variation.
• Implementation of variational method
• Identifying the Hamoltonian
• Guessing trial wave function
• Calculation ground state energy
• Refine the wave function
• Again calculate the ground state energy
• .

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Many body Hamiltonian
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Variational Method
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Optimization of trial wave function
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Example of infinite square well

• Exact ground state wave function

• Trial wave function

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Comparison of ground state energy

• Actual ground state energy

• From variational method
• For lambda 1.72
• 1.00298E0

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Application to many body system
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• End of Talk
• Thank you

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Reference

• JJ Sakurai, Modern Quantum Mechanics, Page
  313-316
• http//phycomp.technion.ac.il/phsorkin/Proposal/p
  roposal/node12.htmltrial_en
• http//www.nyu.edu/classes/tuckerman/quant.mech/le
  ctures/lecture_4/node2.html