Homework Help is Here – Start Your Trial Now!
Science
Advanced Physics
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

icon
Related questions
Question

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.
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.
Expert Solution
steps

Step by step

Solved in 2 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer