## Kinetic energy in the Schrodinger equation

$H_{\psi }=E_{\psi }$

1-D: $E_{TOTAL}\psi (x)=E_{k}\psi (x)+V(x)\psi(x)=-\frac{h^{2}}{8\pi ^{2}m}\frac{d^{2}\psi(x)}{dx^{2}}+V(x)\psi(x)$

ERIKTORRESDisc3C
Posts: 18
Joined: Wed Sep 21, 2016 2:58 pm

### Kinetic energy in the Schrodinger equation

I was reading the section on Schrodinger's equation for wavelength function calculation and found some confusing concepts about it. Why is it that in the Schrodinger equation Kinetic energy is negative in value for calculating wavelength function? Why is the wavelength function's simple form deceptive??

Emi Nakahara 3F
Posts: 21
Joined: Wed Sep 21, 2016 2:57 pm

### Re: Kinetic energy in the Schrodinger equation

Hi Erik,

I've had trouble understanding this as well, but the link below has a helpful section on why wave functions in the Quantum World allow for negative kinetic energy.

http://www.bu.edu/quantum/notes/Quantum ... uation.pdf

In a really rough summary of the section: while in classical mechanics kinetic energy can't ever be negative, in the Schrodinger equation it can be either positive or negative. When the wavefunction is negative, its slope also becomes more and more negative, moving away from the zero line (while with positive kinetic energy, the wave oscilllates on the zero line). It's only another way of describing the wave's direction towards more negative values.