Superposition of Quantum Harmonic Oscillator Eigenstates: Expectation Values and Uncertainties

This Demonstration studies a superposition of two quantum harmonic oscillator eigenstates in the position and momentum representations. The superposition consists of two eigenstates , where and is the Hermite polynomial; the representations are connected via . The top-left panel shows the position space probability density , position expectation value , and position uncertainty . The top-right panel shows the momentum space probability density , momentum expectation value , and momentum uncertainty . The lower two panels show the real and imaginary parts of the wavefunction.