1. The problem statement, all variables and given/known data Consider a quantum mechanical particle moving in a potential V(x) = 1/2mω2x2. When this particle is in the state of lowest energy, A: it has zero energy B: is located at x = 0 C: has a vanishing wavefunction D: none of the above 2. Relevant equations 3. The attempt at a solution Ok from what i know, all energy levels of the particle travelling through the harmonic potential are discrete, and as i understand, the lowest of these discrete energies is the ground state energy but i don't quite understand how this energy is determined? The ground state energy is not zero right? Because if the ground state energy was zero then there would be no wave function in the 1st place right? Also the ground state wave function of the particle when normalised forms a probability density in the form of an upside down porabola almost with exponential decay on both sides, from this you can conclude that the particle is most likely to be at the center or (x=0), so i think the correct answer is B, is my understanding and answer correct or not? If not can someone explain where im going wrong please.