Harmonic Oscillator
- ΔxΔpx=ℏ(n+12)
Particle in a box
- ΔxΔpx=ℏ2√n2π23−2
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 ℏ 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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