How to Solve Schrödinger's Equation using Separation of Variables

We solve Schrödinger's Equation using the separation of variables technique. This is a straightforward mathematical approach that begins with an assumption that the solution to the equation be of a product form. This allows one to separate variables, and obtain a solution to the temporally dependent component of the product solution via integration. Solution is found to be a complex inverse exponential!

Animations were made using the Python-based animation engine of 3Blue1Brown, Manim.

Songs:
Otis - Lambert
Mandal - Lambert
Sad Seine - Lambert

Tags:
#physics
#quantum
#quantumphysics
#quantummechanics
#schrodinger
#schrodingersequation
#schrodingerscat
#differential
#differentialequations
#linear
#homogenous
#mathematics
#math
#manim
#3blue1brown
#3b1b
#science
#mathanimations
#physicsanimations
#physicshomework
#physicsmajor
#undergrad
#collegephysics
#wave
#probability
#particle
#tunneling
#superposition
#electron
#eigenstates
#energy
#Heisenberg
#Bohrmodel
#deBroglie
#Planck's
#photons
#waveparticle
#light
#interference
#diffraction
#differential
#math
#solving
#solve
#schrodinger
#mathematics
#science
#ansatz
#ode
#pde
#partial
#separation
#variables
#classical

[janetterry]

love the quality, keep making more! im taking quantum this fall

[davidrandell]

QM classicalized in 2010: Juliana Mortenson website Forgotten Physics uncovers the ‘hidden variables ‘ and constants and the bad math of Wien, Schrodinger, Heisenberg, Einstein, Debroglie, Planck, Bohr etc.

[shivamrastogi]

What if one of the variables is constantly changing due to different speeds generating different amounts of energy within space

[nebby]

4:08 nice video i am just curious as to why there isnt a constant on the left side of the equation when intergrating? thank you

[jaspalrawat]

Can you understand schrodinger equation

[oosmanbeekawoo]

Hehey! You remember somebody was telling you Manim is overkill for this video?
Scratch that! I think Manim is aesthetic, coloured and hence guideful in presenting equations, compared to pen and paper. Coincidentally, it had a legitimate use in your graph.
Anyway.. the last 30seconds, what is it and how do I do it?