Energy units in the potential well problem

[BlackMelon]

Homework Statement

(Please look at the attached file too)

In one dimension time independent potential well, I want to know what is a suitable unit for energy (electron volts or joule)

Homework Equations

The Attempt at a Solution

In the attached picture, I've tried to analyze each variable's unit. I did this in two cases:
1) when I substitute energy terms in eV
2) when I'm doing so in joule

I substituted units into Schrödinger's Equation and I got 1=1 when I plugged energy with joule. (Please look at the bottom of the attachment)
After I've done this, I thought that the SI unit should be used so energy should be in joule. I plugged all available value in the equation but constants (coefficients) in the equation went crazy! Instead, energy in electron volt gave me much simpler equation to solve.

Thank you

 

[Orodruin]

What units you use have no physical significance and does not matter as long as you do it consistently.

Apart from that, it is not clear exactly what you are trying to do and your attachment appears to be very bad quality. This is why you should write everything out in your post rather than attaching images.

 

[BlackMelon]

Please check the link below. This time you can zoom the picture without losing quality. (Sorry, I'm not good at writing these equation and potential wall on a forum.) I wonder why an equation in SI units side is very hard to solve. Are those equations in SI (Joule) and in electron volts correct?

http://www.mediafire.com/view/if6kjlcj0923518/ASK2.jpg

 

[BvU]

I sympathize: typing all this out in TeX is a load of work.
From what I can read comfortably now, you do a dimension check. Such a check doesn't concern itself with factors like 1.6$\;\times\;$10^-19 !
And yes, working in eV is a lot more comfortable, especially if the energies given are already in eV !

Not to scare you, but theorists like Oro can live comfortably in a world where $e = \hbar = c = 1$. They'd go even more crazy if they wouldn't do that :)
And, to given them due credit: it all comes out fully correct !