United Kingdom

Linkin Park Albums. Linkin Park- Meteora. 1. Donâ€™t Stay. 2. Somewhere I Belong. 3. Hit The Floor. Meteora Links.
Linkin Park’s Meteora is the last of their studio albums – and the only with Chester Bennington. The album is – as expected – produced by Rick Rubin.
1. Don’t Stay. 2. Somewhere I Belong. 3. Hit The Floor. 4. If I Have To Go. 5. Easier To Run. 6. Learning. 7.. 8. Say Goodbye. 9. Living In Oblivion. 10. The Truth In Black And White. 11. Hysteria.
Linkin Park: Enjoy! Tracklist: Don’t Stay. Get Offline. Somewhere I Belong… Hysteria. Hit The Floor. What I’ve Done. Meteora.Q:

Does the harmonic oscillator Hamiltonian have a GUP?

Does the harmonic oscillator Hamiltonian $H=-\frac{\hbar^2}{2m} abla^2+ \frac{1}{2}m \omega^2 r^2$ have a generalized uncertainty principle (GUP)?
I know that the harmonic oscillator Hamiltonian has both a minimal length and a minimal momentum uncertainty, but does this imply a GUP?

A:

The solution of the harmonic oscillator satisfies the Heisenberg uncertainty principle, which clearly does not lead to a modified uncertainty principle. The reason is that, as shown by Sudarshan, the evolution of pure states is unitary, therefore the Heisenberg uncertainty principle is a necessary condition for a unitary evolution.

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