Why can't we use negative values of n in the 1D particle in a box system?

[Thejas15101998]

In the 1D particle in a box system why don't we take negative integer values of n besides the positive integer values? Well I thought about it and I think the reason is that during derivation we get ka=n (wavelength ) and thus n being negative implies that wavelength is negative hence contradiction.

 

[drvrm]

I think the reason is that during derivation we get ka=n (wavelength ) and thus n being negative implies that wavelength is negative hence contradiction.

what is n?
Iis it related to k= n.pi/L or n.pi/a if a is the width of the box
moreover this condition is due to the acceptable wave function (solution of the Schrödinger equation) being zero at the boundary
i.e. at x=0 and x=a
and which dynamical variable is being quantised ?
Is it energy state ?
and if its energy ,then it may be proportional to n^2 rather than n.

 

[DrClaude]

Quantum states are uniquely defined up to a complex phase factor. What difference is there between ±n?

 

[jtbell]

In the 1D particle in a box system why don't we take negative integer values of n besides the positive integer values?

How does the wave function change for e.g. the second eigenstate if you replace n = +2 with n = -2? Does this make any difference in physically measurable quantities?

 

[Thejas15101998]

Here we are considering the time independent Schrödinger equation.

 

[Thejas15101998]

This may not make any difference in the physically measurable that is probability.