It is conventional to set the potential energy at equilibrium to zero, which means that the energy of the ground state is not zero, see http://en.wikipedia.org/wiki/Quantum_harmonic_oscillatorRoodles01 said:I realize that at ground state of a harmonic oscillator the energy will be at zero.
Expectation value of what?Roodles01 said:I'm assuming that the expectation value will also be at zero.
The expectation value at ground state is a concept in quantum mechanics that represents the average value of a physical quantity in the lowest possible energy state of a system.
The expectation value at ground state is calculated by taking the integral of the wave function squared over all possible values of the physical quantity.
The expectation value at ground state is important because it provides a way to predict the behavior of a system in its lowest energy state, which is often the most stable and commonly observed state.
Yes, the expectation value at ground state can be negative. This indicates that the most probable value of the physical quantity in the ground state is less than zero.
The uncertainty principle states that it is impossible to know both the exact position and momentum of a particle. The expectation value at ground state can help to determine the most probable value of a particle's position or momentum, but it cannot give a precise measurement due to the inherent uncertainty in quantum mechanics.