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.
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.
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Pls answer no. 4
![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?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa333d004-1932-4977-abf4-2dc78ad969d1%2F5f44f998-648d-4ef8-a7db-606c15035990%2F2t9pkmd_processed.jpeg&w=3840&q=75)
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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