A coherent state, also known as a Glauber state or a "squeezed quantum state", is an eigenfunction of the harmonic oscillator annihilation operator , where for simplicity. The eigenstates of (a nonhermitian operator) are given by , where are the harmonic-oscillator eigenstates. These coherent states are solutions of the eigenvalue equation with energy expectation values . The eigenvalues can be complex numbers but we restrict them here to real values. This average energy has a form analogous to the harmonic oscillator eigenvalues . The latter are represented by horizontal lines within the potential-energy parabola. The probability density for the wavepacket representing works out to , shown as a blue Gaussian. As the time variation is run, the wavepacket oscillates so that its peak moves between the classical turning points. The wavepacket remains localized in the lowest energy state, when .