The discussion revolves around determining whether the state u(x) = Bxe^[(x^2)/2] is an energy eigenstate of a harmonic oscillator described by the potential V(x) = 1/2*K*X^2. Participants are examining the implications of negative energy solutions in quantum mechanics and the normalization of the wave function.
The discussion is ongoing, with participants providing feedback on calculations and clarifying misunderstandings. There is a focus on the conditions under which the state could be considered an energy eigenstate, and some guidance is offered regarding the mathematical steps involved in solving for energy.
Participants note that the quantum harmonic oscillator typically requires non-negative energy eigenvalues, which raises questions about the validity of the proposed state. There is also mention of the requirement for n to be a non-negative integer, which is relevant to the discussion of energy eigenstates.
No it isn't. Try that again.Relativeee said:The Attempt at a Solution
So the way i did this was, to find if the state is an energy eigenstate of the system i checked to see if it satisfied the time independent Schrödinger equation. After all of the Calculations , came up with, 3- 2E/hw = 0, and the definition of E is E = (n+1/2)hw, so the only way for this solution to be satisfied is if the energy is negative, -2 to be exact.
That's not very exact. If 3 - 2 E/hbar*ω = 0 and you solve for E, what do you get? Hint: Move -2 E/hbar*ω over to the right side and change its sign.Relativeee said:After all of the Calculations , came up with, 3- 2E/hw = 0, and the definition of E is E = (n+1/2)hw, so the only way for this solution to be satisfied is if the energy is negative, -2 to be exact.
OK, in that case, we can perhaps help you if you show the work that led you to that expression.Relativeee said:Oh my goodness i apologize, i meant to put 3 + 2E/hw