Wie lautet die allgemeine Form der Schrödingergleichung für ein Teilchen in einem Potential V(r)V(r)?

iℏ𝜕𝜕tΨ(r⃗,t)=[−ℏ22m∇2+V(r⃗,t)]Ψ(r⃗,t)i ℏ the fraction with numerator partial and denominator partial t end-fraction cap psi open paren modified r with right arrow above comma t close paren equals open bracket negative the fraction with numerator ℏ squared and denominator 2 m end-fraction nabla squared plus cap V open paren modified r with right arrow above comma t close paren close bracket cap psi open paren modified r with right arrow above comma t close paren𝑖ℏ𝜕𝜕𝑡Ψ(𝑟⃗,𝑡)=−ℏ22𝑚∇2+𝑉(𝑟⃗,𝑡)Ψ(𝑟⃗,𝑡)<!--Sv6Kpe[]--><!--Sv6Kpe[]-->

|ℏ²/2𝑚*∇²+𝑉(𝑟⃗)|*𝜓(𝑟⃗)=𝐸𝜓(𝑟⃗)<!--Sv6Kpe[]-->