The variance in position for harmonic oscillator in its ground * state is

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The variance in position for
harmonic oscillator in its ground
* state is
Transcribed Image Text:The variance in position for harmonic oscillator in its ground * state is
Expert Solution
Step 1

Variance (σ2) be defined as,

σ2=x2-x2

Here,

<x2> is the expectation value of x2.

<x> is the expectation value of x.

Step 2

Now, the ground state function of harmonic oscillator be defined as,

ψ0x=mωħπ14exp-mω2ħx2

Step 3

Therefore, the expectation value of x be calculated as,

x=-ψ0*xxψ0xdx=-mωħπ14exp-mω2ħx2xmωħπ14exp-mω2ħx2dx=mωħπ12-xexp-mωħx2dx=0                                            -aaOdd Function=0

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