Derivation of Time Dependent Schrodinger Equation

[Peter Yu]

Hi All,
I have problem in understanding one step in the derivation of the time dependent Schrödinger Equation. Please see attached file page 2 (marked in red). Most grateful if someone can help!
Peter Yu
(This is from Quantum Mechanics The Theoretical Minimum Page 99-102)

 

[ShayanJ]

$(I+i\epsilon H^\dagger)(I-i\epsilon H)=I \Rightarrow I-i\epsilon H+i\epsilon H^\dagger +\epsilon^2H^\dagger H =I \Rightarrow -i\epsilon H+i\epsilon H^\dagger +\epsilon^2H^\dagger H =0$
Now if you ignore the $\epsilon^2$ term and divide by $i\epsilon$, you get what you're after.

 

[Peter Yu]

Hi Shyan,
Many Many thank for your help!
Regards,
Peter Yu