In the context of quantum mechanics, the ground state of a harmonic oscillator does not have an energy of zero when considering the total energy, as the potential energy is conventionally set to zero at equilibrium. The ground state energy is actually a non-zero value, specifically \(\frac{1}{2}\hbar\omega\), where \(\hbar\) is the reduced Planck's constant and \(\omega\) is the angular frequency. The expectation value of the position or momentum in the ground state is indeed zero, but the total energy remains non-zero.
PREREQUISITESStudents and professionals in physics, particularly those focusing on quantum mechanics, as well as researchers interested in the properties of harmonic oscillators and their applications in various fields.
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.