create a presentation to display the results of your research. The report should be a powerpoint or slide.

All work should be typed with double-spacing and 11 pt Arial font. You will be graded on the evidence of work, mathematical detail

and understanding, proper exposition and neatness, time management, and organization of ideas. Your work should also be

supported with properly labeled and embedded plots and equations. Any references used should be cited as well.

Structure:

A suggested outline of the final report include:

Title page (including Title, Names, Abstract), Introduction to Problem (Statement and Background)

.Formulation of Model and Method of Solution

Solution Results (Analytical, Numerical, Plots of Solutions)

The presentation includes: Discussion/Results (Summary and Discussion of Solution)

References

Answered 4 days AfterMar 09, 2022

Spherically Symmetric Solutions to Schrödinger's Equation for the Hydrogen Atom

Spherically

Symmetric

Solutions to

Schrödinger’s

Equation fo

the Hydrogen

Atom

Tannaz Anvari

Spherically Symmetric Solutions to

Schrödinger’s Equation for the Hydrogen

Atom

Tannaz Anvari

March 10, 2022

1 / 1

Spherically

Symmetric

Solutions to

Schrödinger’s

Equation fo

the Hydrogen

Atom

Tannaz Anvari

Outline

2 / 1

Spherically

Symmetric

Solutions to

Schrödinger’s

Equation fo

the Hydrogen

Atom

Tannaz Anvari

Only one frame

Problem Statement

In quantum mechanics one is interested in determining

the wave function and energy states of an atom. These

are determined from Schrödinger’s equation. In the

case of the hydrogen atom, it is possible to find wave

functions ψ that are functions only of r , the distance

from the proton to the electron. Such functions are

called spherically symmetric and satisfy the simple

equation

3 / 1

Spherically

Symmetric

Solutions to

Schrödinger’s

Equation fo

the Hydrogen

Atom

Tannaz Anvari

Only one frame

1

d

dr2

(rψ) =

−8mπ2

h2

(

E +

e20

)

ψ,

where e20,m, and h are constants and E , also a

constant, represents the energy of the atom, which we

assume here to be negative. With these details in mind,

we set out to answer some questions on the subject.

4 / 1

Spherically

Symmetric

Solutions to

Schrödinger’s

Equation fo

the Hydrogen

Atom

Tannaz Anvari

Only one frame

(a) Show that with the substitutions

=

h2

4π2me20

ρ,E =

2π2me40

h2

ϵ,

where ϵ is an negqtive constant, the equation the

problem statement reduces to

d2(ρψ)

dρ2

= −

(

ϵ+

2

ρ

)

ρψ.

5 / 1

Spherically

Symmetric

Solutions to

Schrödinger’s

Equation fo

the Hydrogen

Atom

Tannaz Anvari

Only one frame

In order to solve this, we simply substitute the ansatzs

for E and r in the differential equation to get

(4π2me20)

2

h4

1

ρ

d

dρ2

(ρψ) =

−8mπ2

h2(

2π2me40

h2

ϵ+

4π2me20

h2

e20

ρ

)

ψ,

=⇒

(4π2me20)

2

h4

1

ρ

d

dρ2

(ρψ) = −

(4π2me20)

2

h4

(

ϵ+

2

ρ

)

ψ

=⇒ d

dρ2

(ρψ) = −

(

ϵ+

2

ρ

)

ρψ

Thus, we’ve obtained the required differential equation.

6 /...

Spherically

Symmetric

Solutions to

Schrödinger’s

Equation fo

the Hydrogen

Atom

Tannaz Anvari

Spherically Symmetric Solutions to

Schrödinger’s Equation for the Hydrogen

Atom

Tannaz Anvari

March 10, 2022

1 / 1

Spherically

Symmetric

Solutions to

Schrödinger’s

Equation fo

the Hydrogen

Atom

Tannaz Anvari

Outline

2 / 1

Spherically

Symmetric

Solutions to

Schrödinger’s

Equation fo

the Hydrogen

Atom

Tannaz Anvari

Only one frame

Problem Statement

In quantum mechanics one is interested in determining

the wave function and energy states of an atom. These

are determined from Schrödinger’s equation. In the

case of the hydrogen atom, it is possible to find wave

functions ψ that are functions only of r , the distance

from the proton to the electron. Such functions are

called spherically symmetric and satisfy the simple

equation

3 / 1

Spherically

Symmetric

Solutions to

Schrödinger’s

Equation fo

the Hydrogen

Atom

Tannaz Anvari

Only one frame

1

d

dr2

(rψ) =

−8mπ2

h2

(

E +

e20

)

ψ,

where e20,m, and h are constants and E , also a

constant, represents the energy of the atom, which we

assume here to be negative. With these details in mind,

we set out to answer some questions on the subject.

4 / 1

Spherically

Symmetric

Solutions to

Schrödinger’s

Equation fo

the Hydrogen

Atom

Tannaz Anvari

Only one frame

(a) Show that with the substitutions

=

h2

4π2me20

ρ,E =

2π2me40

h2

ϵ,

where ϵ is an negqtive constant, the equation the

problem statement reduces to

d2(ρψ)

dρ2

= −

(

ϵ+

2

ρ

)

ρψ.

5 / 1

Spherically

Symmetric

Solutions to

Schrödinger’s

Equation fo

the Hydrogen

Atom

Tannaz Anvari

Only one frame

In order to solve this, we simply substitute the ansatzs

for E and r in the differential equation to get

(4π2me20)

2

h4

1

ρ

d

dρ2

(ρψ) =

−8mπ2

h2(

2π2me40

h2

ϵ+

4π2me20

h2

e20

ρ

)

ψ,

=⇒

(4π2me20)

2

h4

1

ρ

d

dρ2

(ρψ) = −

(4π2me20)

2

h4

(

ϵ+

2

ρ

)

ψ

=⇒ d

dρ2

(ρψ) = −

(

ϵ+

2

ρ

)

ρψ

Thus, we’ve obtained the required differential equation.

6 /...

SOLUTION.PDF## Answer To This Question Is Available To Download

- Math 1104C, 1104J: Test # 1, Due Feb. 9 11:59, 2022Directives:• This document has 3 pages (including this page).• This assignment is due on March 16th at 11:59 p.m. on Brightspace.• The...SolvedMar 16, 2022
- MATH2004C Assignment 2Last Name: First Name:Student ID:• You may either write your answers on a copy of this assignment, or on your ownpaper or on your electronic devices (you do not need to...SolvedMar 07, 2022
- Please confirm if what I did is correct for my attached assignment.Scenario: We send out appointment reminder calls to our customers for their upcoming appointments with our cliniics. Since patients...SolvedMar 06, 2022
- UntitledExercise 5 (Getting started)a) Compute the expressions 127/13+pi, exp(3)*13i and exp(pi*i).b) Let C =0.521 und B =2 3 2−0.25 0 −13/5 −3/5 0. Determine...SolvedMar 01, 2022
- 1. Vectors in the Plane and Space, Rotations of Axes and Transitions in the Plane.2. Planar Curves and Conic Sections, Applications to Area and the Length of Curves.3. Polar Coordinates and...SolvedFeb 17, 2022
- 2/11/22, 2:07 PM Quiz: M3.C1: Quiz: On Modules 1-2https://sit.instructure.com/courses/58579/quizzes/68968/take 1/3M3.C1: Quiz: On Modules 1-2Started: Feb 11 at 2:06pmQuiz InstructionsThis...SolvedFeb 12, 2022
- 202201 Math 122 Assignment 2Due: Friday, Feb. 11, 2022 at 23:59. Please submit on your section’s Crowdmark page.There are five questions of equal value (worth a total of 45 marks), and one bonus...SolvedFeb 08, 2022
- Assignment #1: Balanced Scorecard for an Accounting Firm. York, Mason, and Chase (YMC) is an accounting firm in Miami. The firm has had a very loose and relaxed management style that has served it...SolvedDec 31, 2021
- 12. TEAM PROJECT. Divergence Theorem and Poten-tial Theory. The importance of the divergence theo-rem in potential theory is obvious from (7)–(9) and Theorems 1-3. To emphasize it further, consider...SolvedDec 31, 2021
- 1. For the ODE(x - 1)y" - xy + y = 0, x > 1,(a) Verify that yl = ex is a solution, (b) Use the method of reduction-of-order to find a second (linearly independent) solution, (c) Verify linear...SolvedDec 31, 2021

Copy and Paste Your Assignment Here

Disclaimer: The reference papers provided by TAE serve as model papers for students and are not to be submitted as it is. These papers are intended to be used for research and reference purposes only.

Copyright © 2022. All rights reserved.