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Q3:3 A particle is initially represented by a state which is one of the eigenfunctions {on (x)} of a hamiltonian operator H, namely ø1, whose normalised form is given by 2 1 (z) = 7!/2* exp The eigenvalue for this eigenfuncțion is 3. (a) What is the mean or average value of x for this state?

Q3:3 A particle is initially represented by a state which is one of the eigenfunctions {on (x)} of a hamiltonian operator H, namely ø1, whose normalised form is given by 2 1 (z) = 7!/2* exp The eigenvalue for this eigenfuncțion is 3. (a) What is the mean or average value of x for this state?

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Q3:3 A particle is initially represented by a state which is one of the eigenfunctions {on (x)} of a hamiltonian operator H, namely ø1, whose normalised form is given by 2 01 (x) = - 7!/2 exp 2 The eigenvalue for this eigenfuncțion is 3. (a) What is the mean or average value of r for this state?
Transcribed Image Text:Q3:3 A particle is initially represented by a state which is one of the eigenfunctions {on (x)} of a hamiltonian operator H, namely ø1, whose normalised form is given by 2 01 (x) = - 7!/2 exp 2 The eigenvalue for this eigenfuncțion is 3. (a) What is the mean or average value of r for this state?
Expert Solution
Step 1

The given state of the particle is represented by the following wave function

ϕ1(x)=2π1/2x exp-x22

The average value of x or the expectation value of x for the particle in this state will be found using this wave function as

<x>=∫-∞+∞ϕ1(x)*xϕ1xϕ1(x)* is the complex conjugate of ϕ1(x)

Since the given wave function is real, ϕ1(x)*=ϕ1(x)

Thus, the expectation value for x is written as

<x>=∫-∞+∞ϕ1(x)2x

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