How to solve schrodinger equation of diatomic rigid rotator?
Answers
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How do you solve Schrodinger’s equation?
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5 ANSWERS
Francesco Maddalena
Francesco Maddalena, Ph.D Physics, University of Groningen
Answered Feb 13, 2018 · Upvoted by Enrique Morell, B.S. Physics, Pierre and Marie Curie University (2018) and Balu Sreedhar, Integrated MSc Physics, Pondicherry University (2019) · Author has 5.3k answers and 2.8m answer views
The Schordinger Equation is a differential equation.
Considering just the non-relativistic one:
HΨ(r,t)=iℏδδtΨ(r,t)HΨ(r,t)=iℏδδtΨ(r,t)
[−ℏ22m∇2+V(r,t)]Ψ(r,t)=iℏδδtΨ(r,t)[−ℏ22m∇2+V(r,t)]Ψ(r,t)=iℏδδtΨ(r,t)
where ∇2=δ2δx2+δ2δy2+δ2δx2∇2=δ2δx2+δ2δy2+δ2δx2 is the Lapalce operator (in this case in 3 dimensions).
The objective of the differential equation is to find Ψ(r,t)Ψ(r,t) which is a function of position (the vector rr) and time (tt)
Usually first you solve for stationary states, meaning:
[−ℏ22m∇2+V(r,t)]Ψ(r,t)=EΨ(r,t)[−ℏ22m∇2+V(r,t)]Ψ(r,t)=EΨ(r,t)
where EE is a constant (the Energy)