Using an argument based on the general form of the Schrödinger equation, explain why if \psi (x) is a solution to the Schrödinger equation, then A\psi(x) must also be a solution if A is a constant.I saw an explanation for this from another posted question, but this person put the explanation in numerical/equation form. Is there any way someone can explain the answer to this question in words (NON numerical/equation form)?

Answers

Answer 1

Answer:

From a mathematical point of view, the Schrödinger Equation is a LINEAR partial differential equation, as is a partial differential equation that is defined by a linear polynomial in the solution and its derivatives.

For a linear differential equation, if you got two different solutions $\psi$ and $\phi$ , then the linear combination $\alpha \psi + \beta \phi$ , where $\alpha$ and $\beta$ are scalars, is also a solution.

This also is valid for only one solution (think of the other solution as equal to zero, $\phi = 0$ ). So, as the Schrödinger Equation is a Linear partial differential equation, then if $\psi$ is a solution, then $A \psi$ must also be a solution.

This is extremely important for physicist, as let us know that the superposition principle is valid.

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A driver drives for 30.0 minutes at 80.0 km/h, then 45.0 minutes at 100 km/h. She then stops 30 minutes for lunch. She then travels for 30 minutes at 80 km/h. (a) Sketch a plot of her displacement versus time and speed versus time. (b) Calculate her average speed.

Answers

Answer:

b) 68,9 km/h a) picture

Explanation:

In this problem, since velocity is expressed in km/h and time in minutes, we have to convert either time to hours or velocity to km/min. It is easier to use hours.

Using this formula we pass time to hours:

$t_(hours)=t_(min)*(1 h)/(60 min)\n30min*(1 h)/(60 min)=0,5h\n45min*(1 h)/(60 min)=0,75h$

Now we can plot speed vs time (image 1). The problem says that the driver uses constant speed, so all lines have to be horizontal.

Using the values of the speed we calculate the distance in each interval

$d=v*t\n80km/h*0.5h=40km\n100km/h*0.75h=75km$

Using these values and the fact that she was having lunch in the third one (therefore stayed in the same position), we plot position vs time, using initial position zero (image 2, distance is in km, not meters).

Finally, we compute the average speed with the distance over time:

$v_(average)=(155km)/(2.25h)=68.9km/h$

The knot at the junction is in equilibrium under the influence of four forces acting on it. The F force acts from above on the left at an angle of α with the horizontal. The 5.7 N force acts from above on the right at an angle of 50◦ with the horizontal. The 6.2 N force acts from below on the right at an angle of 44◦ with the horizontal. The 6.7 N force acts from below on the left at an angle of 43◦ with the horizontal.1. What is the magnitude of the force F?
2. What is the angle a of the force F in the figure above?

Answers

(a) The magnitude of the force F acting on the knot is 5.54 N.

(b) The angle α of the force F is 54.4⁰.

The given parameters:

F force at α
5.7 N force at 50⁰
6.2 N force at 44⁰
6.7 N force at 43⁰

The net vertical force on the knot is calculated as follows;

$F_y = Fsin(\alpha) + 5.7 sin(50) - 6.2 sin(44) - 6.7 sin(43)\n\nF_y = F sin(\alpha) -4.51\n\nFsin(\alpha) = 4.51$

The net horizontal force on the knot is calculated as follows;

$F_x = -F cos(\alpha) + 5.7 cos(50) + 6.2cos(44) - 6.7cos(43)\n\nF_x = -Fcos(\alpha) + 3.22\n\nFcos(\alpha) = 3.22$

From the trig identity;

$sin^2 \theta + cos^ 2 \theta = 1\n\n$

$(Fsin(\alpha))^2 + (Fcos(\alpha))^2 = (4.51)^2 + (3.22)^2\n\nF^2(sin^ 2\alpha + cos^2 \alpha) = 30.71\n\nF^2(1) = 30.71\n\nF = √(30.71) \n\nF = 5.54 \ N$

The angle α of the force F is calculated as follows;

$Fsin(\alpha) = 4.51\n\nsin(\alpha) = (4.51)/(F) \n\nsin(\alpha ) = (4.51)/(5.54) \n\nsin(\alpha ) = 0.814\n\n\alpha = sin^(-1)(0.814)\n\n\alpha = 54.5 \ ^0$

Find the image uploaded for the complete question.

Learn more about net force here:brainly.com/question/12582625

The knot is in equilbrium, so there is no net force acting on it. Starting with the unknown force and going clockwise, denote each force by F₁, F₂, F₃, and F₄, respectively. We have

F₁ + F₂ + F₃ + F₄ = 0

Decomposing each force into horizontal and vertical components, we have

F cos(180º - α) + (5.7 N) cos(50º) + (6.2 N) cos(-44º) + (6.7 N) cos(-137º) = 0

F sin(180º - α) + (5.7 N) sin(50º) + (6.2 N) sin(-44º) + (6.7 N) sin(-137º) = 0

Recall that cos(180º - x) = - cos(x) and sin(180º - x) = sin(x), so these equations reduce to

F cos(α) ≈ - 3.22 N

F sin(α) ≈ 4.51 N

(1) Recall that for all x, sin²(x) + cos²(x) = 1. Use this identity to solve for F :

(F cos(α))² + (F sin(α))² = F ² ≈ 30.73 N² → F ≈ 5.5 N

(2) Use the definition of tangent to solve for α :

tan(α) = sin(α) / cos(α) ≈ 1.399 → α ≈ 126º

or about 54º from the horizontal from above on the left of the knot.

Tell whether the statement below is a scalar or a vector

Answers

Answer:

1. Scalar

2.Vector

3. Scalar

4. Vector

5.Scalar

6.Scalar

7.Vector

8.Vector

9.Scalar

10.Scalar

11.Scalar

12. Vector

13.Scalar

Explanation:

Scalar refers to magnitude, and Vectors include magnitude with directions.

Calculate the ionization potential for C+5 ( 5 electrons removed for the C atom) and in addition compute the wavelength of the transition from n=3 to n= 2.

Answers

Answer:

Ionization potential of C⁺⁵ is 489.6 eV.

Wavelength of the transition from n=3 to n=2 is 1.83 x 10⁻⁸ m.

Explanation:

The ionization potential of hydrogen like atoms is given by the relation :

$E = (13.6Z^(2) )/(n^(2) ) eV$ .....(1)

Here E is ionization potential, Z is atomic number and n is the principal quantum number which represents the state of the atom.

In this problem, the ionization potential of Carbon atom is to determine.

So, substitute 6 for Z and 1 for n in the equation (1).

$E = (13.6*(6)^(2) )/(1^(2) )$

E = 489.6 eV

The wavelength (λ) of the photon due to the transition of electrons in Hydrogen like atom is given by the relation :

$(1)/(\lambda) =RZ^(2)[(1)/(n_(1) ^(2))-(1)/(n_(2) ^(2) )]$ ......(2)

R is Rydberg constant, n₁ and n₂ are the transition states of the atom.

Substitute 6 for Z, 2 for n₁, 3 for n₂ and 1.09 x 10⁷ m⁻¹ for R in equation (2).

$(1)/(\lambda) =1.09*10^(7) *6^(2)[(1)/(2 ^(2))-(1)/(3 ^(2) )]$

$(1)/(\lambda)$ = 5.45 x 10⁷

λ = 1.83 x 10⁻⁸ m

What best describes the bromide ion that forms

Answers

Answer:

it A

Explanation:

Its a negative ion that hss one less valence electron than a netural bromine atom

Describe the objects that make up Saturn's rings. Your answer should include the range of sizes of objects in the rings, and the composition of the at least the outer layers of the objects.

Answers

Saturn's rings are made of billions of pieces of ice, dust and rocks. Some of these particles are as small as a grain of salt, while others are as big as houses.

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