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4 years ago

6

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]4 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>

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Which values from the given replacement set make up the solution set of the inequality? m+7 < 18 ; {8,9,10,11}

NNADVOKAT [17]

A because if you simplify the inequality you get m<11 The only answer which has values under 11 is A

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3 years ago

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Determine if true:<br> 3^3x4=108

AlekseyPX

Answer:

<u>True</u>

Step-by-step explanation:

3³ x 4

= 3 x 3 x 3 x 4

= 9 x 12

= 108

<u>True</u>

8 0

2 years ago

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A sphere and a cylinder have the same radius and height. The volume of the cylinder is 21m. what is the volume of the sphere.

Goshia [24]

Answer:

The volume of the sphere is 14m³

Step-by-step explanation:

Given

Volume of the cylinder = $21m^3$

Required

Volume of the sphere

Given that the volume of the cylinder is 21, the first step is to solve for the radius of the cylinder;

<em>Using the volume formula of a cylinder</em>

The formula goes thus

$V = \pi r^2h$

Substitute 21 for V; this gives

$21 = \pi r^2h$

Divide both sides by h

$\frac{21}{h} = \frac{\pi r^2h}{h}$

$\frac{21}{h} = \pi r^2$

The next step is to solve for the volume of the sphere using the following formula;

$V = \frac{4}{3}\pi r^3$

Divide both sides by r

$\frac{V}{r} = \frac{4}{3r}\pi r^3$

Expand Expression

$\frac{V}{r} = \frac{4}{3}\pi r^2$

Substitute $\frac{21}{h} = \pi r^2$

$\frac{V}{r} = \frac{4}{3} * \frac{21}{h}$

$\frac{V}{r} = \frac{84}{3h}$

$\frac{V}{r} = \frac{28}{h}$

Multiply both sided by r

$r * \frac{V}{r} = \frac{28}{h} * r$

$V = \frac{28r}{h}$ ------ equation 1

From the question, we were given that the height of the cylinder and the sphere have equal value;

This implies that the height of the cylinder equals the diameter of the sphere. In other words

$h = D$ , where D represents diameter of the sphere

Recall that $D = 2r$

So, $h = D = 2r$

$h = 2r$

Substitute 2r for h in equation 1

$V = \frac{28r}{2r}$

$V = \frac{28}{2}$

$V = 14$

Hence, the volume of the sphere is 14m³

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3 years ago

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Find the slope of the line passing through the points (8,-6) and (1, -2).

Alik [6]

Step-by-step explanation:

The slope of the line is -4/7.

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3 years ago

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How do you do this <br>.

mars1129 [50]

The slope of the line on the graph represents Pete's speed. That slope is 8 miles/hour.

Paul walks 2 miles in 0.4 hours, so walks at (2/0.4) miles/hour = 5 miles/hour.

a) Pete is moving at a greater rate.

b) At 8 miles per hour, it takes Pete (2 mi)/(8 mi/h) = 1/4 h = 15 minutes to get to school. If Pete leaves 5 minutes later than Paul, he will reach school 20 minutes after Paul starts, while Paul is still 4 minutes away from the school.

Yes, Pete will catch Paul before they get to school.

6 0

3 years ago