Potential Energy Operator subjected to a Coulombic Potential

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SUMMARY

The discussion centers on constructing the potential energy operator for a particle subjected to a Coulombic potential, defined as \(\phi = \frac{q}{4\pi\epsilon r}\). The total energy of the system is expressed as the sum of kinetic and potential energy, represented by the equation Total Energy = Kinetic + Potential. The kinetic energy operator is given by \(-\frac{h^2}{2m}\frac{d^2\psi}{dx^2}\), and the discussion emphasizes that the potential energy operator can be constructed similarly to the kinetic energy operator.

PREREQUISITES
  • Understanding of quantum mechanics principles
  • Familiarity with the Schrödinger equation
  • Knowledge of Coulombic potential and its mathematical representation
  • Basic skills in differential equations
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  • Study the derivation of the potential energy operator in quantum mechanics
  • Explore the application of the Schrödinger equation to systems with Coulombic potentials
  • Learn about the implications of kinetic and potential energy operators in quantum systems
  • Investigate the role of boundary conditions in solving differential equations related to potential energy
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Students and professionals in quantum mechanics, physicists working with atomic models, and researchers focusing on potential energy in quantum systems will benefit from this discussion.

benrogers7511
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Looking for help with "Construciting the potential energy operator of a particle subjected to a Coulombic potential?"


Coulombic Potential: [tex]\phi[/tex] = q/(4[tex]\pi[/tex][tex]\epsilon[/tex]r)

Total Energy= (Kinetic + Potential) = [-(h^2/2m)(d^2psi/dx^2) + U(x)]


Kinetic Energy Operator = -(h^2/2m)(d^2[tex]\psi[/tex]/dx^2)

I am looking for the potential energy operator
 
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Well, how is the kinetic energy operator built ? In the same way you can build the potential energy one.
 

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