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1. Which of the following functions are eigenfunctions of the operator and which of ? Give the eigenvalues where appropriate. a. y = eikx b. y = cos(kx) C. y = e2

1. Which of the following functions are eigenfunctions of the operator and which of ? Give the eigenvalues where appropriate. a. y = eikx b. y = cos(kx) C. y = e2

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1. Which of the following functions are eigenfunctions of the operator and which of ? Give the eigenvalues where appropriate. a. y = ekx b. y = cos(kx) C. y = eax^2 2. True or False. a. (A+B)f(x) is always equal to Af(x) + Bf(x) b. A[f(x) + g(x)] is always equal to Âf(x) + Âg(x) c. BÊt(x) is always equal to CBf(x) 3. Calculate the probability of finding the particle in a one-dimensional box of length a at n=1 in the interval 0.100a to 0.250a. wave function for a particle in a box: nnx sin 4. A particle of mass M is constrained to be on a line along the z axis perpendicular to the earth's surface in a gravitational field where g is the acceleration of gravity. a. Write the Schrödinger equation for this system. b. Determine the boundary conditions that must be satisfied by the wavefunction for this system. 5. If a hexatriene molecule absorbs light of 2500 Å to change a m electron from n=1 to n=2, what is the length of the molecule?
Transcribed Image Text:1. Which of the following functions are eigenfunctions of the operator and which of ? Give the eigenvalues where appropriate. a. y = ekx b. y = cos(kx) C. y = eax^2 2. True or False. a. (A+B)f(x) is always equal to Af(x) + Bf(x) b. A[f(x) + g(x)] is always equal to Âf(x) + Âg(x) c. BÊt(x) is always equal to CBf(x) 3. Calculate the probability of finding the particle in a one-dimensional box of length a at n=1 in the interval 0.100a to 0.250a. wave function for a particle in a box: nnx sin 4. A particle of mass M is constrained to be on a line along the z axis perpendicular to the earth's surface in a gravitational field where g is the acceleration of gravity. a. Write the Schrödinger equation for this system. b. Determine the boundary conditions that must be satisfied by the wavefunction for this system. 5. If a hexatriene molecule absorbs light of 2500 Å to change a m electron from n=1 to n=2, what is the length of the molecule?
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