iℏ⋅(∂Ψ(x,t))/(∂t)=-ℏ^2/2m⋅(∂^2Ψ(x,t))/(∂x^2)
(This is how the average conversation about quantum mechanics generally goes:)
Person 1: Omg like literally iℏ⋅(∂Ψ(x,t))/(∂t)=-ℏ^2/2m⋅(∂^2Ψ(x,t))/(∂x^2)
Person 2: Right! Lmao it's just ∂Ψ(x,t)=Ae^(i(kx-ωt))
Person 1: Exactly! And iℏ⋅(∂Ψ(x,t))/(∂t)=iℏ⋅(∂Ae^(i(kx-ωt)))/(∂t)=ℏωAe^(i(kx-ωt))
Person 2: Hahaha! -ℏ^2/2m⋅(∂^2Ψ(x,t))/(∂x^2)=-ℏ^2/2m⋅(∂^2Ae^(i(kx-ωt)))/(∂x^2)
Person 1: Yeah and it's like -(ikℏ^2)/2m⋅(∂Ae^(i(kx-ωt)))/(∂x)=-ℏ^2/2m⋅(∂^2Ψ(x,t))/(∂x^2)=-ℏ^2/2m⋅(∂^2Ae^(i(kx-ωt)))/(∂x^2)
Person 2: Bro I was thinking the same thing, as soon as she walked in my mind just went (ℏ^2⋅k^2)/2m⋅Ae^(i(kx-ωt))= -(ikℏ^2)/2m⋅(∂Ae^(i(kx-ωt)))/(∂x)=-ℏ^2/2m⋅(∂^2Ψ(x,t))/(∂x^2)=-ℏ^2/2m⋅(∂^2Ae^(i(kx-ωt)))/(∂x^2)
Person 1: Pfffftttt!!! (ℏ^2⋅k^2)/2m=ℏω
Person 2: Lol yeah man, great shit right there... So anyway, how's Jack?
Person 1: Omg like literally iℏ⋅(∂Ψ(x,t))/(∂t)=-ℏ^2/2m⋅(∂^2Ψ(x,t))/(∂x^2)
Person 2: Right! Lmao it's just ∂Ψ(x,t)=Ae^(i(kx-ωt))
Person 1: Exactly! And iℏ⋅(∂Ψ(x,t))/(∂t)=iℏ⋅(∂Ae^(i(kx-ωt)))/(∂t)=ℏωAe^(i(kx-ωt))
Person 2: Hahaha! -ℏ^2/2m⋅(∂^2Ψ(x,t))/(∂x^2)=-ℏ^2/2m⋅(∂^2Ae^(i(kx-ωt)))/(∂x^2)
Person 1: Yeah and it's like -(ikℏ^2)/2m⋅(∂Ae^(i(kx-ωt)))/(∂x)=-ℏ^2/2m⋅(∂^2Ψ(x,t))/(∂x^2)=-ℏ^2/2m⋅(∂^2Ae^(i(kx-ωt)))/(∂x^2)
Person 2: Bro I was thinking the same thing, as soon as she walked in my mind just went (ℏ^2⋅k^2)/2m⋅Ae^(i(kx-ωt))= -(ikℏ^2)/2m⋅(∂Ae^(i(kx-ωt)))/(∂x)=-ℏ^2/2m⋅(∂^2Ψ(x,t))/(∂x^2)=-ℏ^2/2m⋅(∂^2Ae^(i(kx-ωt)))/(∂x^2)
Person 1: Pfffftttt!!! (ℏ^2⋅k^2)/2m=ℏω
Person 2: Lol yeah man, great shit right there... So anyway, how's Jack?
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