Suppose a molecule is prepared in way that it is not an eigenfunction of the Hamiltonian....

 

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Suppose a molecule is prepared in way that it is not an eigenfunction of the Hamiltonian. The energy is not an eigenvalue, and the molecule is in a superposition of states corresponding to several energies. This superposition is called a wave packet. Superimpose 10 sine wavefunctions 10 4(1,4)=sin(not + ) n=1 no are frequencies of the states; n are integers, take to be 3 x 1013 s-1. t is time. ois phase, let = 0. (a) Show with a graph that this superposition can form a well-focused "packet" at various times t. This is also the basis of the Fourier principle. Take the phases all to be zero and do this by a computer (Excel spreadsheet is fine). (b) The focusing of the wave packet recurs at specific intervals. What is the first value of t in seconds that there is a recurrence of the well-focused packet happen, given the specific value of @? 10 k=1 (c) Now add the 10 sine functions with a different phase, o, of two radians, sin(not + ). Explain what happens. Suppose a molecule is prepared in way that it is not an eigenfunction of the Hamiltonian. The energy is not an eigenvalue, and the molecule is in a superposition of states corresponding to several energies. This superposition is called a wave packet. Superimpose 10 sine wavefunctions 10 4(1,4)=sin(not + ) n=1 no are frequencies of the states; n are integers, take to be 3 x 1013 s-1. t is time. ois phase, let = 0. (a) Show with a graph that this superposition can form a well-focused "packet" at various times t. This is also the basis of the Fourier principle. Take the phases all to be zero and do this by a computer (Excel spreadsheet is fine). (b) The focusing of the wave packet recurs at specific intervals. What is the first value of t in seconds that there is a recurrence of the well-focused packet happen, given the specific value of @? 10 k=1 (c) Now add the 10 sine functions with a different phase, o, of two radians, sin(not + ). Explain what happens.