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3 years ago

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Problems that require solving the three-dimensional schrödinger equation can often be reduced to related one-dimensional problem

s. an example of this would be the particle in a cubical box. consider a cubical box with rigid walls (i.e., u(x,y,z)=∞ outside of the cube) and edges of length l. the general solution for this problem is

1 answer:

dusya [7]3 years ago

8 0

The wavefunction for a particle in a one-dimension box is a well-known problem, which has as a solution:

Ψ(x) = √(2/l) sin (nπx/l)

When the box has three dimensions, the general solution is simply the multiplication of the solutions for each dimension, therefore:

Ψ(x) = K · sin (n_x·π·x / l) · sin (n_y·π·y / l) · sin <span>(n_z·π·z / l)</span>

You might be interested in

Please help 100 points and brainlest for all the answers

masha68 [24]

Answer:

See explanation

Step-by-step explanation:

Q1. The graph of given data is attached.

The relationship is directly proportional as the line connecting all points is straight line passing through the origin.

For every 1 unit change in x, the change of y is 16.

Therefore, the equation that represents this line is

$y=16x$

If $x=10,$ then $y=16\cdot 10=160$ square feet.

Q2. Yes, the relationship shows the direct proportionality as the line connecting all points is straight line passing through the origin (see second attached graph).

For every 1 unit change in x, the change of y is 0.45.

Therefore, the equation of the line is

$y=0.45x$

Q3. Yes, the relationship shows the direct proportionality as the line connecting all points is straight line passing through the origin.

Find the constant of proportionality:

If x = 2, y = 25, then

when x = 1, y = 12.5

so k = 12.5

and the equation of the line is

$y=12.5x$

When $x=14,$ then $y=12.5\cdot 14=175$

Hence, the cost of 14 tickets is $175

Q4. This table does not show the direct variation because

if x = 500 and y = 40, then

for x = 100, y is $40\div 5=8$

and for x = 700, y must be $7\cdot 8=56$ not 50.

Hence, this relationship does not show the direct proportionality between x and y.

Q5. This elationship shows the direct proportionality as the line connecting all points is straight line passing through the origin.

The constant of proportionality is $k=1.75$

The equation of proportionality is $y=1.75x$

When $y=28,$ then

$28=1.75x\\ \\x=\dfrac{28}{1.75}\\ \\x=16$

This means for $28 you could buy 16 ice cream scoops.

Q6. The line passes through the point (2,61), so the constant of proportionality is

$k=\dfrac{61}{2}=30.5$

The equation of proportional relationship is

$y=30.5x$

When $y=274.50,$ then

$274.50=30.5x\\ \\x=\dfrac{274.5}{30.5}\\ \\x=9$

This means you could buy 9 tickets for $274.50

Q7. The equation which represent proportional relationship should have the equation of the form

$y=kx$

Circle all equations in this form:

$y=5x\\ \\p=0.5m\\ \\y=\dfrac{1}{2}x\\ \\M=3n\\ \\y=2x$

Q8. A relationship between two variables in which one is a constant multiple of the other. In particular, when one variable changes the other changes in proportion to the first. If y is directly proportional to x, the equation is of the form y = kx (where k is a constant).

This means that the graph of direct variation is always a straight line passing through the origin (because x = 0 and y = 0 satisfy the equation for all k).

Not all lines represent the proportional relationship. Only those, which pass through the origin.

4 0

2 years ago

Read 2 more answers

Use the converse of the pythagorean theorem to determine whether the triangle with the given vertices is a right triangle. (2, 1

weeeeeb [17]

B.
if it's is a right angle triangle, two of the x-coordinate of the points must be the same however with the points given, we can tell that the x coordinates are different , the two points are not vertical hence it does not form a right angle triangle.

4 0

3 years ago

2. Which of the following is not an example of

Mariulka [41]

Answer:

B. 200

Step-by-step explanation:

A perfect square is the multiplication of two equal integers such as 1*1=1, 2*2=4, 3*3=9. From the examples, 1, 4, 9 are perfect square.

Non perfect square numbers are 1*2=2,

3*1=3,

5*1=5,

3*2=6,

6*1=6,

7*1=7

Examples of perfect squares:

1*1=1

2*2=4,

3*3=9,

4*4= 16,

5*5=25,

6*6=36,

7*7=49,

8*8=64,

9*9=81,

10*10=100,

11*11=121,

12*12=144,

13*13=169,

14*14=196,

15*15=225 and so on

8 0

2 years ago

Which of the following numbers represents the fraction 8/9 to the nearest percent?

jekas [21]

The number that presents 8/9 to the nearest percent is .89.

6 0

2 years ago

Felix's parents opened a savings

Crazy boy [7]

The money in the Felix's account will be $6798 when he is 21.

<u>Step-by-step explanation:</u>

It is given that,

The amount deposited is $2000.
The account earns 6% compound interest.
It is compounded annually for 21 years.

<u>To find the money in Felix's account after 21 years :</u>

The formula used here is,

⇒ $A = P(1+r/n)^{nt}$

where A is the amount after 21 years.

P is the initial amount deposited ⇒ P = 2000
r is the rate ⇒ r = 0.06
n is the number of times interest is compounded per year⇒ n = 1
t is the time period ⇒ t = 21

⇒ $2000(1+0.06/1)^{21\times 1}$

⇒ $2000(1.06)^{21}$

⇒ $2000\times3.399$

⇒ $6798$

Therefore, The money in the Felix's account will be $6798 when he is 21.

4 0

3 years ago