What is the potential energy function for a 1D Harmonic Oscillator

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Presentation transcript:

What is the potential energy function for a 1D Harmonic Oscillator with force constant K? (A) V(x) = a+bK (B) V(x) = sin(Kx) (C) V(x) = ½ K x3 (D) V(x) = ½ K x2 (E) V(x) = e-Kx

What is the potential energy function for a 1D Harmonic Oscillator with force constant K? (A) V(x) = a+bK NO... linear curve (B) V(x) = sin(Kx) NO...periodic curve (C) V(x) = ½ K x3 NO... asymmetric (D) V(x) = ½ K x2 YES!!...Parabola (E) V(x) = e-Kx NO...asymmetric, exponential V(x) x V(x) x V(x) x V(x) x V(x) x

Could the ground state of the Harmonic Oscillator in principle be at the bottom of the well? (A) Yes, there is no reason to have it higher, since the potential is not a constant (different from the PIB) (B) No, because of Heisenberg’s Uncertainty Principle.

Could the ground state of the Harmonic Oscillator in principle be at the bottom of the well? (A) Yes, there is no reason to have it higher, since the potential is not a constant (different from the PIB). Wrong, this was not the reason for nonzero E1 in the PIB. (B) No, because of Heisenberg’s Uncertainty Principle. Correct. p  0 and x  0