The quantum bouncer represents the classical vertical motion under gravity. Consider a quantum bouncer ofmass m moving along the vertical. Choose the vertical axis as the x-axis. The potential energy of the particle isV(x)= mgx1. Sketch the potential energy diagram2. Write the time-independent Schrodinger equation and show that it can be transformed to thed?yform of Airy equation= xydx²3. Write the boundary conditions.4. Sketch in the above potential energy diagram the energies and the eigenfunctions of the groundstate (energy Eo), the first excited state (energy E,), and the second excited state (energy E2),.In your sketch, indicate the points of classical maximum heights.

(a) Given: The potential energy of the particle is V(x)=mgx. Introduction: The Schrödinger equation…

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 = xy dx² 3. Write the boundary conditions.

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 = xy dx² 3. Write the boundary conditions.