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Expansion of Shrodinger Equation

Posted: Sun Oct 09, 2016 11:20 am
Hi,

I was reading through Chapter 1 and saw that the book included an expanded version of the Schrodinger equation ( $\large -\frac{hbar^2}{2m}* \frac{d^2\Psi }{dx^2} + V(x)\Psi = E\Psi$ ). I was wondering what this meant and if we needed to know it for quizzes or exams?

Thanks!

Re: Expansion of Shrodinger Equation  [ENDORSED]

Posted: Sun Oct 09, 2016 6:16 pm
The entire part in the parenthesis is just the Hamiltonian. You do not need to worry about solving it or anything, just know that it is the Hamiltonian which, when acted upon a wavefunction, returns the energy of the wavefunction. The same equation is usually simplified to the following:

$H\varphi=E\varphi$

Re: Expansion of Shrodinger Equation

Posted: Sun Oct 09, 2016 9:03 pm
What is meaning of the Hamiltonian? I mean, how does it relate in Schrodinger's equation? Is it just the change in the wave function?

Re: Expansion of Shrodinger Equation

Posted: Sat Oct 21, 2017 11:59 am
The Hamiltonian is the energy that is enacted upon a wavefunction that changes gradually.