The variance in position for harmonic oscillator in its ground * state is
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Variance (σ2) be defined as,
Here,
<x2> is the expectation value of x2.
<x> is the expectation value of x.
Now, the ground state function of harmonic oscillator be defined as,
Therefore, the expectation value of x be calculated as,
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- Consider a system in a state Y If the x component of 2, m angular momentum L is measured on it, find the possible values the measurement will yield and their correponding probabilities.Consider an electron in a 2D harmonic trap with force constants kxx = 232 N/m and kyy = 517 N/m. List the energies of the lowest 10 eigenfunctions.# quantum mechanical particde in a harmonic osci lator potential has the initial wave function y,)+4,(x), where Y. and Y, are the real wavefunctions in the ground and fist exci ted state of the harmonic osciclator Hamiltonian- for Convenience we take mzhzw= 1 for the oscillator- What ở the probabilpty den sity of finding the par ticke at x at time tza?