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Solv­ing the Sch­rodinger Equa­tion is Quantum Mech­an­ics 101. Unfor­tu­nately, some­times instruct­ors get things off to a bad start by not­ing the solu­tions — as though they came from thin air!!! 😥

Per­son­ally, this threw me — when it shouldn’t! I want you to be com­fort­able and con­fid­ent with the solu­tions — so you can ‘pull them from the sky’! 

Solv­ing this Dif­fer­en­tial Equa­tion is SIMPLE!! Though con­vin­cing you may take 6 videos — you’ll be able to solve this in less than 60 seconds (as illus­trated in video 7).

Get your Quantum Mech­an­ics off to a strong start here.

Happy stud­ies!

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# Title Remarks
1 Ter­min­o­logy & Setup Access: [MM_Product_Data id=‘43’ name=‘price’ doFormat=‘true’]
  • 4 minutes 28 seconds.
  • List of vari­ous titles/labels used.
  • Defin­i­tion of the TISE using wave­func­tion & Dir­ac notation.
  • Brief descrip­tion of the Hamilto­ni­an Operator.
  • Ter­min­o­logy of the Sch­rodinger Eigen­value Equation.
2 Hamilto­ni­an Energy Oper­at­or Access: [MM_Product_Data id=‘44’ name=‘price’ doFormat=‘true’]
  • 2 minutes 47 seconds.
  • What is an Operator.
  • What is the instruc­tion relat­ing to the Hamilto­ni­an Operator.
  • How to apply the Hamilto­ni­an Oper­at­or to a wavefunction.
  • The com­plete Time Inde­pend­ent Sch­rodinger Equation.
3 Defin­ing the Con­stants Access: [MM_Product_Data id=‘45’ name=‘price’ doFormat=‘true’]
  • 4 minutes 49 seconds.
  • Using primed nota­tion for deriv­at­ives in order to express the TISE in a neat­er fashion.
  • Writ­ing the TISE in the form required for the Char­ac­ter­ist­ic Equation.
  • Defin­ing the con­stants k (the wavenumber).
  • How the defin­i­tion of the con­stant k will affect the func­tion­al form of the TISE solutions.
  • Show you the two com­mon ways to write the TISE using dif­fer­ent defin­i­tions of the constants.
4 Cosine & Sine Solu­tions Access: [MM_Product_Data id=‘46’ name=‘price’ doFormat=‘true’]
  • 6 minutes 23 seconds.
  • Using the Char­ac­ter­ist­ic Equa­tion to solve the TISE (with the first defin­i­tion of the wavenumber).
  • The gen­er­al solu­tion to the Char­ac­ter­ist­ic Equa­tion (a com­plex number).
  • The gen­er­al solu­tion to the TISE.
  • Why the solu­tion to the TISE is often a lin­ear com­bin­a­tion of cosines and sines.
5 Com­plex Expo­nen­tial Solutions

Access: [MM_Product_Data id=‘47’ name=‘price’ doFormat=‘true’]

  • 4 minutes 6 seconds.
  • Re-writ­ing the tri­go­no­met­ric solu­tions to the TISE as com­plex expo­nen­tial functions.
  • Using Euler’s Equations.
6 Real Expo­nen­tial Solu­tions Access: [MM_Product_Data id=‘48’ name=‘price’ doFormat=‘true’]
  • 5 minutes 19 seconds.
  • Using the Char­ac­ter­ist­ic Equa­tion to solve the TISE (with the second defin­i­tion of the wavenumber).
  • The gen­er­al solu­tion to the Char­ac­ter­ist­ic Equa­tion (a com­plex number).
  • The gen­er­al solu­tion to the TISE.
  • Why the solu­tion to the TISE is often a lin­ear com­bin­a­tion of real expo­nen­tial functions.
7 Solved in 60 Seconds Access: [MM_Product_Data id=‘49’ name=‘price’ doFormat=‘true’]
  • 2 minutes 12 seconds.
  • Now that we under­stand how to solve the TISE — we no longer need to com­plete all of the neces­sary steps.
  • Imme­di­ately know what the solu­tions to the TISE are — just by look­ing at it!!
8 Recap (Free)
  • 6 minute recap of the Learn­ing Points from all pre­vi­ous 7 videos.

 

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