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Solving 1D Schrödinger Equation [Part 4] Stationary States
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The method of separation of variables is used to solve the Schrödinger equation in 1D with a potential V(x) that has no time dependence. We turn 1 partial differential equation into 2 ordinary differential equations. The time dependent ODE is solved, giving the exponential form of φ(t). In the previous video, the time-independent Schrödinger equation is examined to determine 𝜓(x). In this video, solutions of the form 𝛹(x,t)=𝜓(x)φ(t) are shown to be stationary states.
#Quantum
#Schrödinger
#StationaryState
Konstantin Lakic
The method of separation of variables is used to solve the Schrödinger equation in 1D with a potential V(x) that has no time dependence. We turn 1 partial differential equation into 2 ordinary differential equations. The time dependent ODE is solved, giving the exponential form of φ(t). In the previous video, the time-independent Schrödinger equation is examined to determine 𝜓(x). In this video, solutions of the form 𝛹(x,t)=𝜓(x)φ(t) are shown to be stationary states.
#Quantum
#Schrödinger
#StationaryState
Konstantin Lakic
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