I Help with Math in Quantum Mechanics: Variational Method

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mody mody
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Hello
i read a quantum mechanics part and found a part of mathematics that i am not a familiar with it so i need a help how to get the equation at the bottom of the attached photo (the mathematics of applying variational method )
 

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Hello mody2

The one numbered (2) ? Or the one ending in ##\sqrt\alpha## ?
Starting from where ?
What makes you use the term 'variational method' ? Any context ? Where was it mentioned before ?
 
i want second equation that ended by root of alpha
starting by just following the sequence given at the photo

that was mentioned here
https://arxiv.org/pdf/1510.07813.pdf
 
mody mody said:
starting by just following the sequence given at the photo
I mean where, at what point, at what level, do I have to start ? Do you have any experience at all with a QM course, the hydrogen atom wave functions, the ##Y_{lm}## ? If they are not the 'usual spherical harmonics' to you, I suggest you take a QM textbook and see how far you can come.

Where, exactly, do you get stuck when you work out this <H> ? Show your steps in detail and someone will help you put the last pieces of the puzzle together. Starting from 1+1=2 is really too tedious.
 

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