Friday, 28 September 2018

quantum mechanics - Why does DeltaxDeltapx increase linearly with n for stationary states?



Harmonic Oscillator



  • ΔxΔpx=(n+12)


Particle in a box



  • ΔxΔpx=2n2π232


Similarly, the cone potential V(x)=|x| and the exponential potential V(x)=exp(|x|) have been shown to have ΔxΔpx grow linearly with n.


We notice that for small n the product is of the same order of magnitude as and for large n it grows linearly with it:




  • Is that behavior expected? If yes, then why?

  • Is this a general behavior for any stationary states of any system?




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