The quantum bouncer represents the classical vertical motion under gravity. Consider a quantum bouncer of mass m moving along the vertical. Choose the vertical axis as the x-axis. The potential energy of the particle is V(x) = mgx 1. Sketch the potential energy diagram 2. Write the time-independent Schrodinger equation and show that it can be transformed to the form of Airy equation d²y = xy dx² 3. Write the boundary conditions. 4. Sketch in the above potential energy diagram the energies and the eigenfunctions of the ground state (energy E.), the first excited state (energy E,), and the second excited state (energy E2),. In your sketch, indicate the points of classical maximum heights.
The quantum bouncer represents the classical vertical motion under gravity. Consider a quantum bouncer of mass m moving along the vertical. Choose the vertical axis as the x-axis. The potential energy of the particle is V(x) = mgx 1. Sketch the potential energy diagram 2. Write the time-independent Schrodinger equation and show that it can be transformed to the form of Airy equation d²y = xy dx² 3. Write the boundary conditions. 4. Sketch in the above potential energy diagram the energies and the eigenfunctions of the ground state (energy E.), the first excited state (energy E,), and the second excited state (energy E2),. In your sketch, indicate the points of classical maximum heights.
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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![The quantum bouncer represents the classical vertical motion under gravity. Consider a quantum bouncer of
mass m moving along the vertical. Choose the vertical axis as the x-axis. The potential energy of the particle is
V(x) = mgx
1. Sketch the potential energy diagram
2. Write the time-independent Schrodinger equation and show that it can be transformed to the
form of Airy equation
d²y
= xy
dx²
3. Write the boundary conditions.
4. Sketch in the above potential energy diagram the energies and the eigenfunctions of the ground
state (energy E.), the first excited state (energy E,), and the second excited state (energy E2),.
In your sketch, indicate the points of classical maximum heights.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1e635da4-036a-4abe-947d-543b63929172%2F2e129872-823f-4297-bf6a-ea2418a0a40f%2Fwh3v2zd_processed.png&w=3840&q=75)
Transcribed Image Text:The quantum bouncer represents the classical vertical motion under gravity. Consider a quantum bouncer of
mass m moving along the vertical. Choose the vertical axis as the x-axis. The potential energy of the particle is
V(x) = mgx
1. Sketch the potential energy diagram
2. Write the time-independent Schrodinger equation and show that it can be transformed to the
form of Airy equation
d²y
= xy
dx²
3. Write the boundary conditions.
4. Sketch in the above potential energy diagram the energies and the eigenfunctions of the ground
state (energy E.), the first excited state (energy E,), and the second excited state (energy E2),.
In your sketch, indicate the points of classical maximum heights.
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