skip to Main Content
contact@universityphysictutorials.com

 

The cal­cu­la­tion of the Wave­func­tions of Hydro­gen was one of the first achieve­ments of Quantum The­ory. Gen­er­ally their deriv­a­tion will be the cul­min­a­tion of an under­gradu­ate course in Quantum Mech­an­ics. In many respects, these deriv­a­tions are a great test of a student’s ground­ing in both phys­ics and math­em­at­ic­al phys­ics. This is because the stu­dent will require a know­ledge both of power series solu­tions to dif­fer­en­tial equa­tions and of course some quantum theory!

Return to Dif­fer­en­tial Equations

Return to Quantum Mechanics

Video # Video Tutori­al Title Remarks
1 The Char­ac­ter­ist­ic Equa­tion 1/2 Deriv­a­tion for solv­ing Second Order Dif­fer­en­tial Equa­tions with con­stant coefficients
2 Intro­duc­tion to Laplace’s Equation One of the most import­ant dif­fer­en­tial equa­tions seen in physics
3 Intro­duc­tion to Sep­ar­a­tion of Variables A very power­ful meth­od for solv­ing dif­fer­en­tial equations
4 Char­ac­ter­ist­ic Equa­tion 2/2 Using the Char­ac­ter­ist­ic Equa­tion to solve dif­fer­en­tial equations
5 Sep­ar­a­tion of Variables Example 1
6 Sep­ar­a­tion of Variables Example 2
7 Sep­ar­a­tion of Variables Example 3
8 Prop­er­ties of Sep­ar­able Solutions Com­plete­ness, and orthogonality
9 Spher­ic­al Polar Coordinates The Sch­rodinger Equa­tion in solved in spher­ic­al polar coordinates
10 The Laplace Equa­tion in Spher­ic­al Coordinates The pre­curs­or to solv­ing the Sch­rodinger Equa­tion for hydrogen
11 The Radi­al Equation The first ordin­ary equa­tion from the meth­od of sep­ar­a­tion of variables
12 The Lapla­cian in Spher­ic­al Coordinates A pretty nasty deriv­a­tion! (mainly here for the sake of completeness)
13 The Azi­muth­al Equa­tion for Hydrogen The second ordin­ary equa­tion from the meth­od of sep­ar­a­tion of variables
14 The Polar Angle Equa­tion for Hydrogen The third ordin­ary equa­tion from the meth­od of sep­ar­a­tion of variables
15 The Sch­rodinger Equa­tion in Spher­ic­al Coordinates Get­ting ready to solve for Hydrogen’s wavefunctions
16 The Radi­al Equa­tion for Hydrogen The most import­ant equa­tion in this section
17 Deriv­a­tion of the Wave­func­tions of Hydrogen The cul­min­a­tion of the section
18 Quantum Num­bers What the quantum num­bers mean!
19 Quantum Num­bers An older ver­sion of video #18; per­haps with a dif­fer­ent viewpoint
20 Quantum States of the Hydro­gen Atom Bring­ing all of the hard work togeth­er in a conclusion
21 Elec­tron Orbitals The fun­da­ment­als of chemistry

 

 

 

kahn academy hydro­gen atom quantum mech­an­ics stat­ist­ics wave­func­tions wave-func­tions deriv­a­tion derive states orbit­al orbit­als elec­tron kahn academy hydro­gen atom quantum mech­an­ics stat­ist­ics wave­func­tions wave-func­tions deriv­a­tion derive states orbit­al orbit­als electron 

Back To Top