# Proof that 1D bound states are non-degenerate without Wave Mechanics

Most proofs I see that all bound states of a quantum system are non-degenerate use the wave-function representation. How can we prove it using only Dirac notation, without resorting to the wave picture?

• Do you mean non-degenerate in your question body? Also, $\psi(x)=\langle x|\psi\rangle$, so couldn't you say the arguments are the same, or maybe I am missing something. Perhaps you could expand on both what you have seen and what you want to be shown. – Aaron Stevens Nov 26 '18 at 4:48
• Yes, my bad. I've already fixed it. – user140323 Nov 26 '18 at 4:50
• Perhaps you might translate as much of this related question to observe that your are very much considering the space dependence of the potential and the wave function involved and wf normalizability. The question is why on earth would you like to abstract away from space features? – Cosmas Zachos Nov 26 '18 at 17:20
• I believe the question would be why not? – user140323 Nov 26 '18 at 17:39
• Why not hike the Alps in flipflops? – Cosmas Zachos Nov 27 '18 at 1:06