Consider a particle which is confined to move along the positive
x-axis, and that has a Hamiltonian
where
is a
positive real constant having the dimensions of energy.
Find the normalized wave function that corresponds to an energy
eigenvalue of . The
function should be finite everywhere along the positive x-axis and
be square integrable.
Homework Answers
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Consider a particle which is confined to move along the positive
x-axis, and that has a...
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Q10 The Hamiltonian of a two-state system is given by H E ( i)- I02)(2 | -i | ¢1)(2 | +i | ¢2) (¢1 1) where , p2) form a complete and orthonormal basis; E is a real constant having the dimensions of energy (a) Is H Hermitian? Calculate the trace of H (b) Find the matrix representing H in the | øı), | 42) basis and calculate the eigenvalues and the eigenvectors of the matrix. Calculate the trace of...
A particle is completely confined to one-dimensional region along the x-axis between the points x =...
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Consider a particle confined to one dimension and positive r with the wave function 0, z<0...
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A particle is confined to a one-dimensional box (an infinite well) on the x-axis between x...
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Consider a particle confined to one dimension and positive z with the wave function 0 where...
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A particle is completely confined to one-dimensional region along the x-axis between the points x = ± L The wave function that describes its state is: SP 10 elsewhere where a and b are (as yet) unknown constants that can be expressed in terms of L Use the fact that the wave function must be continuous everywhere to solve for the constant b. The square of the wave function is a probability density, which means that the area under that...
Consider a particle confined to one dimension and positive r with the wave function 0, z<0 where N is a real normalization constant and o is a real positive constant with units of (length)-1. For the following, express your answers in terms of a: a) Calculate the momentum space wave function. b) Verify that the momentum space wave function is normalized such that (2.4) c) Use the momentum space wave function to calculate the expectation value (p) via (2.5)
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A particle is confined to a one-dimensional box (an infinite well) on the x-axis between x = 0 and x L. The normalized wave function of the particle when in the ground state, is given by A. What is the probability of finding the particle between x Eo, andx,? A. 0.20 B. 0.26 C. 0.28 D. 0.22 E. 0.24
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