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4. Consider a gaussian probability density on the x axis p(x) = A exp[- λ(x-a)² ] λ>0, a, and A are constants (a) Sketch the graph of p(x) (b) Find the normalization constant A (c) Find the expectation values < x >, < x² > and the variance o
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Transcribed Image Text:4. Consider a gaussian probability density on the x axis p(x) = A exp[- λ(x-a)² ] λ>0, a, and A are constants (a) Sketch the graph of p(x) (b) Find the normalization constant A (c) Find the expectation values < x >, < x² > and the variance o
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Step 1: Know the concept:
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Step 2: (a) Sketch the graph of the probability density function:
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Step 3: (b) Calculate the normalization constant of the function:
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Step 4: (c) Calculate the expectation value of the position:
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Step 5: (c) Calculate the expectation value of the square of x:
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Step 6: (c) Calculate the variance of the position:
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Solution
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