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

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Discussion Overview

The discussion revolves around the use of negative integer values of n in the context of the 1D particle in a box system, focusing on the implications for wave functions and quantization in quantum mechanics. Participants explore theoretical aspects, derivations, and the nature of quantum states.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • Some participants suggest that negative values of n lead to negative wavelengths, which they argue creates a contradiction in the derivation of the system.
  • There is a question regarding the relationship between n and the wave number k, specifically whether k is defined as k = nπ/L or nπ/a, where a is the width of the box.
  • Participants discuss the boundary conditions of the wave function, noting that it must be zero at the boundaries (x=0 and x=a), which may influence the quantization of n.
  • One participant raises the point that quantum states are defined up to a complex phase factor, questioning the significance of using ±n.
  • Another participant inquires about the physical implications of substituting n = +2 with n = -2 in the second eigenstate, asking if this affects measurable quantities.
  • It is noted that the discussion is centered on the time-independent Schrödinger equation.
  • One participant suggests that using negative n may not affect physically measurable quantities such as probability.

Areas of Agreement / Disagreement

Participants express differing views on the implications of using negative values of n, with some arguing against it due to contradictions in wavelength, while others question the physical significance of such a distinction. The discussion remains unresolved regarding the overall impact of negative n on measurable quantities.

Contextual Notes

Participants have not reached a consensus on the implications of negative n values, and there are unresolved questions about the relationship between n and the quantization of energy states.

Thejas15101998
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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.
 
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Thejas15101998 said:
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.
 
Quantum states are uniquely defined up to a complex phase factor. What difference is there between ±n?
 
Thejas15101998 said:
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?
 
Here we are considering the time independent Schrödinger equation.
 
This may not make any difference in the physically measurable that is probability.
 

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