ar/ad= 0. (e) Substituthree parts into the rigshow that you get the lethree positive inte gers (1, 2, 3, . ). [Hint: Use sepa-ration of variables, and seek a solution of the form= X(x) Y (y) Z (z). Note that by setting a b = cobtains the cubical box of Example 8.2.]SECTION 8.5 (The Three-DForce Problem)SECTION 8.4 (The Two-Dimensional Central-Force Problem)8.20 The spherical polarfined in Fig. 8.11. Derivefor x, y, and z in terms ofexpressions for r, 0, and8.16 (a) For the two-dimensional polar coordinatesdefined in Fig. 8.7 (Section 8.4), prove the relationsX = r cos and y r sin (8.104)8.21 A point P on the earcoordinates (x, y, z) and(r, 0, ø) (with coordinateis at the earth's center aWhat are the coordinatesof the place Q at the oppoCter through P?(b) Find corresponding expressions for r and interms of x andу.A certain point P in two dimensions has rectangularcoordinates (x, y) and polar coordinates (r, ). Whatare the polar coordinates of the point Q(-x, -y)?Illustrate your answer with a picture.8.17Changes of coordinates in two dimensions (such asthat from x, y to r, ) are much more complicatedthan in one dimension. In one dimension, if we have afunction f(x) and choose to regard x as a function ofsome other variable u, then the derivative of f withrespect to u is given by the chain rule,8.188.22.Substitute the separatecinto the Schrödinger equatyou multiply through byarrange, you get an equat(function of r and 0). Expladf

Question
Asked Nov 12, 2019
3 views

For Problem 8.16, how do I prove the relations and give the correct expressions?

ar/ad= 0. (e) Substitu
three parts into the rig
show that you get the le
three positive inte gers (1, 2, 3, . ). [Hint: Use sepa-
ration of variables, and seek a solution of the form
= X(x) Y (y) Z (z). Note that by setting a b = c
obtains the cubical box of Example 8.2.]
SECTION 8.5 (The Three-D
Force Problem)
SECTION 8.4 (The Two-Dimensional Central-
Force Problem)
8.20 The spherical polar
fined in Fig. 8.11. Derive
for x, y, and z in terms of
expressions for r, 0, and
8.16 (a) For the two-dimensional polar coordinates
defined in Fig. 8.7 (Section 8.4), prove the relations
X = r cos and y r sin (8.104)
8.21 A point P on the ear
coordinates (x, y, z) and
(r, 0, ø) (with coordinate
is at the earth's center a
What are the coordinates
of the place Q at the oppoC
ter through P?
(b) Find corresponding expressions for r and in
terms of x and
у.
A certain point P in two dimensions has rectangular
coordinates (x, y) and polar coordinates (r, ). What
are the polar coordinates of the point Q(-x, -y)?
Illustrate your answer with a picture.
8.17
Changes of coordinates in two dimensions (such as
that from x, y to r, ) are much more complicated
than in one dimension. In one dimension, if we have a
function f(x) and choose to regard x as a function of
some other variable u, then the derivative of f with
respect to u is given by the chain rule,
8.18
8.22.Substitute the separatec
into the Schrödinger equat
you multiply through by
arrange, you get an equat
(function of r and 0). Expla
df
help_outline

Image Transcriptionclose

ar/ad= 0. (e) Substitu three parts into the rig show that you get the le three positive inte gers (1, 2, 3, . ). [Hint: Use sepa- ration of variables, and seek a solution of the form = X(x) Y (y) Z (z). Note that by setting a b = c obtains the cubical box of Example 8.2.] SECTION 8.5 (The Three-D Force Problem) SECTION 8.4 (The Two-Dimensional Central- Force Problem) 8.20 The spherical polar fined in Fig. 8.11. Derive for x, y, and z in terms of expressions for r, 0, and 8.16 (a) For the two-dimensional polar coordinates defined in Fig. 8.7 (Section 8.4), prove the relations X = r cos and y r sin (8.104) 8.21 A point P on the ear coordinates (x, y, z) and (r, 0, ø) (with coordinate is at the earth's center a What are the coordinates of the place Q at the oppoC ter through P? (b) Find corresponding expressions for r and in terms of x and у. A certain point P in two dimensions has rectangular coordinates (x, y) and polar coordinates (r, ). What are the polar coordinates of the point Q(-x, -y)? Illustrate your answer with a picture. 8.17 Changes of coordinates in two dimensions (such as that from x, y to r, ) are much more complicated than in one dimension. In one dimension, if we have a function f(x) and choose to regard x as a function of some other variable u, then the derivative of f with respect to u is given by the chain rule, 8.18 8.22.Substitute the separatec into the Schrödinger equat you multiply through by arrange, you get an equat (function of r and 0). Expla df

fullscreen
check_circle

Expert Answer

Step 1

Draw a figure to represent a point using both polar and Cartesian coordinates.

Y
Р(х, у)
У
-х
М
х
help_outline

Image Transcriptionclose

Y Р(х, у) У -х М х

fullscreen
Step 2

(a)

Consider the right angled triangle OMP.

Write an expression for cosϕ using trigonometry

cos
r
xrcos d
help_outline

Image Transcriptionclose

cos r xrcos d

fullscreen
Step 3

Write an expression for sinϕ u...

sin
yrsin
help_outline

Image Transcriptionclose

sin yrsin

fullscreen

Want to see the full answer?

See Solution

Check out a sample Q&A here.

Want to see this answer and more?

Solutions are written by subject experts who are available 24/7. Questions are typically answered within 1 hour.*

See Solution
*Response times may vary by subject and question.
Tagged in

Science

Advanced Physics

Related Advanced Physics Q&A

Find answers to questions asked by student like you

Show more Q&A add
question_answer

Q: please help, i had the math and mechanical engineering  expert help but they said that this problem ...

A: a)Drag D should increase with the density ρ associated with the fluid as more density will correspon...

question_answer

Q: A conveyor belt is used to send burgers through a grilling machine. If the grilling machine is 1.5 m...

A: Click to see the answer

question_answer

Q: Let vectors A =(2,1,−4), B =(−3,0,1), and C =(−1,−1,2).Calculate the following: What is the angle θA...

A: Write the given vectors in the form of  linear combination of the unit vectors as,

question_answer

Q: A power plant operates at a 25.0% efficiency during the summer when the seawater used for cooling is...

A:  Here Th is the absolute temperature of the hot source and Tc that of the cold sink, usually measure...

question_answer

Q: An equilateral triangular plate with sides 8 m is submerged vertically in water so that the base is ...

A: An equilateral triangular plate with sides 8 m is submerged vertically in water so that the base is ...

question_answer

Q: a) 95 μm  b) 90 μm c) 85 μm  d) 80 μm

A: The intensity of the neutron beam is

question_answer

Q: What is a quantum system?

A: A quantum system is a portion of the whole universe which is taken under consideration to make analy...

question_answer

Q: (10%) Problem 3: Three electric charges, Q1-2 C, Q2-2 C, and Q,--10 C, are shown in the figure, alon...

A: Given:

question_answer

Q: (10%) Problem 6: A conducting spherical shell of inner radius R1 and outer radius R2 has a point cha...

A: A conducting spherical shell of inner radius R1 and outer radius R2. A point charge +q is fixed at t...