In the figure, there is a particle of mass m in a two-dimensional square box. The potential energy function for this system is defined as follows: V(x,y) = 0 x<0 ve y< 0 V (x, y) = {0, 0a ve y >a V(x.y) = 0. a (a) Write the Hamilton (total energy) operator and V(x.y) = 0 the Schrödinger equation of the system
In the figure, there is a particle of mass m in a two-dimensional square box. The potential energy function for this system is defined as follows: V(x,y) = 0 x<0 ve y< 0 V (x, y) = {0, 0a ve y >a V(x.y) = 0. a (a) Write the Hamilton (total energy) operator and V(x.y) = 0 the Schrödinger equation of the system
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In the figure, there is a particle of mass m in a two-dimensional square box. The
potential energy function for this system is defined
as follows
![In the figure, there is a particle of mass m in a two-dimensional square box. The
potential energy function for this system is defined
as follows:
y4
x< 0 ve y<0
0<xsa ve 0<y<a
V(x.y) = 0
o,
V (x, y) ={0,
x>a ve y >a
V(x.y) = 0.
a
(a) Write the Hamilton (total energy) operator and
V(x.y) = 0
the Schrödinger equation of the system.
(b) Find the wave function outside of this box with a
a
side a based on the probability density.
V(x.y) = 0
(c) Write the Schrödinger equation for this box with
potential V (x, y) = 0.
(d) Using the method of separation of variables,
write the equation obtained in c as terms containing different variables. (The total energy
of the system can be written as the sum of the energies of the x and y variables,
E = Ex + Ey.)
(e) Using the wave function and energy equations of the particle in a one-dimensional
box, obtain the normalized wave function and energy equation for this system (particle
system in a square box).
(f) It can be assumed that the 6 T-electrons of the benzene molecule move inside a square
box with a side length of 4 Å. Calculate the wavelength of light the molecule must
absorb for a T-electron to pass from its ground state to its excited state.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F237c0969-eab5-4a0e-bb12-a0c6bb07d13b%2F5dc81b57-5fdd-4ef7-95f6-b18cbc76d348%2Fu7wbawk_processed.png&w=3840&q=75)
Transcribed Image Text:In the figure, there is a particle of mass m in a two-dimensional square box. The
potential energy function for this system is defined
as follows:
y4
x< 0 ve y<0
0<xsa ve 0<y<a
V(x.y) = 0
o,
V (x, y) ={0,
x>a ve y >a
V(x.y) = 0.
a
(a) Write the Hamilton (total energy) operator and
V(x.y) = 0
the Schrödinger equation of the system.
(b) Find the wave function outside of this box with a
a
side a based on the probability density.
V(x.y) = 0
(c) Write the Schrödinger equation for this box with
potential V (x, y) = 0.
(d) Using the method of separation of variables,
write the equation obtained in c as terms containing different variables. (The total energy
of the system can be written as the sum of the energies of the x and y variables,
E = Ex + Ey.)
(e) Using the wave function and energy equations of the particle in a one-dimensional
box, obtain the normalized wave function and energy equation for this system (particle
system in a square box).
(f) It can be assumed that the 6 T-electrons of the benzene molecule move inside a square
box with a side length of 4 Å. Calculate the wavelength of light the molecule must
absorb for a T-electron to pass from its ground state to its excited state.
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