Suppose we have the following vectorial equation c = na x b where n is a constant, and c, a, b are vectors Givens n = -1 a = 2i – j

a) Determine the direction and size of the vector c if b = 2i

b) Determine the direction and size of the vector c if b = 2k

c) Determine the direction and size of the vector c if b = 2i – k

I really need the step by step for this. If you could, please write legibly.

Thank you Greatly!

in this problem we are interested in the time-evolution of the states in the infinite square potential well. The time-independent stationary state wave functions are denoted as ψn(x) (n = 1, 2, . . .).

(a) We know that the probability distribution for the particle in a stationary state is time-independent. Let us now prepare, at time t = 0, our system in a non-stationary state

Ψ(x, 0) = (1/√( 2)) (ψ1(x) + ψ2(x)).

Study the time-evolution of the probability density |Ψ(x, t)|^2 for this state. Is it periodic in the sense that after some time T it will return to its initial state at t = 0? If so, what is T? Sketch, better yet plot (by using some software), |Ψ(x, t)|^2 for 3 or 4 moments of time t between 0 and T that would nicely display the qualitative features of the changes, if any.

(b) Let us now prepare the system in some arbitrary non-stationary state Ψ(x, 0). Is it true that after some time T, the wave function will always return to its original spatial behavior, that is,

Ψ(x, T) = Ψ(x, 0)

(perhaps with accuracy to an inconsequential overall phase factor)? If so, what is this quantum revival time T? Compare to (a). And why do you think it was possible to have it in this system for an arbitrary state?

(c) Think now about the revival time for a classical particle of energy E bouncing between the walls. Assuming the positive answer to (b), if we were to compare the classical revival behavior to the quantum revival behavior, when these times would be equal?

Need help with Part C!

Design a carefully scaled and drawn Minkowski diagram depicting two reference frames P (x and t) and Q (x' and t') with Q moving at a speed of 0.6c in the positive x-direction with respect to P.

i) If event A occurs at x=1 and t=1 while event B occurs at x=1 t=2, determine the interval of time between these events as measured by an observer in Q. Suggest two other events and use them to demonstrate reciprocity of time dilation. Show the space-time interval is the same for P and Q

ii) If a meter stick is at rest in Q between x=1 and x=2, determine the length measured by an observer in P.

If I have a positively charged surface and bring it near to a plasma, what would happen? Will both the electrons and protons behave in the same way? (compare their accelerations).

at the beginning, a stagnant bomb explodes and breaks into 3 pieces.in this case a)is linear momentum maintained?please explain. b) is kinetic energy conserved? please explain.

1. On a planet, the acceleration due to gravity is only 7.2 m/s². A person living on that planet throws a football at 10 m/s at an angle of 48 degrees to the horizontal. The person is standing, so the ball launches from an initial height of 1.8 meters above the ground. (Ignore any air resistance here.)

1. What maximum height from the ground would the ball reach?
2. What would be the flight time before the ball gets back to the ground?

Explain the method of determining the charge-to-mass ratio (e/m) in the Thomson experiment.

An interstitial in the lattice structure puts the surrounding bonds lattice in tension or compression? How does this stress affect movements of dislocations? Use figures/schematics to explains.

Explain the model of blackbody. Present and explain Wien’s and Stefan’s laws regarding the blackbody radiation. Explain Planck’s hypothesis of energy quanta.

what is the angular separation between a star at Right Ascension 6hr and Declination 60 degrees and another star at Right Ascension 0hr and Declination 60 degrees? and also please explain what is angular separation?

Derive the barometric formula which shows in an isothermal atmosphere the pressure as a function of height.

Choose the correct answer/s.

1.) In an interference experiment, monochromatic light from a laser is passed through two parallel slits separated by d.  An interference pattern is formed on the screen placed at a distance R from the screen. If the separation distance between the slits is doubled, which of the following is true?

2.)

Which of the following statements is NOT true about a double-slit interference pattern?

3.)

If you compare the single-slit pattern and the double-lit pattern, which of the following is correct?

8.)

In a diffraction experiment, monochromatic light from a laser is passed through a slit of width a.  A diffraction pattern is formed on the screen placed at a distance x from the screen. Which of the following statements is true?

an 10 kg object is hung from a spring attached to a fixed support. The spring constant of the spring is k=40 Nm**(-1) (I mean to the power of -1) Suppose an external downward force of magnitude f(T) = 20 e **(-2t) N is applied to the object, and damping due to air resistence occurs with damping constant beta = 40 N s m **(-1). Let y(t) denote the distance in meters of the object below its equilibrium position at time t seconds. Take the gravitational constant to be g=9.8 m.s**(-2). a) Draw a diagram of the system, showing all forces acting on the object, assuming object is above the equilibrium position and moving down. Include the direction and magnitude of each force.

b) state the equation of motion of object.

c) Find the general solution to the equation of motion.

d) Assume that the object initially starts at the equilibrium position with the velocity of 2 m.s**(-1) upwards

i. Find the position of the object at any time.

ii. At what times, if any, is the object located at its equilibrium position?