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Wavefunction

Particle in an infinite tube

a) A particle with mass m and energy E is inside a square with tube infinite potential barriers at x=0, x=a, y=0 and y=a. The tube is infinitely long in the z direction. Inside the tube v=0. The particle is moving in the +z direction solve the Schrodinger equation to derive the allowed wave functions for this particle. Do not tr

Semi-infinite square well.

Consider the semi-infinite square well given by V(x)=-Vo<0 for 0<=x<=a and V(x)=0 for x>a. There is an infinite barrier at x=0. A particle with mass m is in a bound state in this potential energy E<=0. a) solve the Schroedinger Eq to derive phi(x) for x=>0. Use the appropriate boundary conditions and normalized the wave funct

Zero Point Energy

A baseball is confined between two thick walls at a distance. 0.5M a part. calculate the zero point energy of the baseball. My book has no examples for zero point energy and it might be on my test. I need a outline of the solution please.

Semi-Infinite Square Well Potential

Consider the semi-infinte square well potential shown in diagram of attachment. a. Given that the energy eigenvalue for the first excited state E2=0 (i.ie u2 is at the edge of being bound) find the width a of the well in terms of m, h and Vo. (Hint consider the continuity of u2 at x=a). b. Calculate the energy eigenvalue E1 fo

Orbital Radius of the Proton's Wavefunction

In a hydrogen atom, the electron and proton can be considered to 'orbit' each other about their common center of mass. a. If the electron wavefunction has a mean orbital radius equal to 0.527 Angstroms (the Bohr radius) what is the mean orbital radius of the proton's wavefunction? b. If the hydrogen atom is suddenly ionized (i

Particle of mass m in a one-dimensional impenetrable box

A particle of mass m is in a one-dimensional impenetrable box extending from x = 0 to x = a. At t = 0, its wavefunction is given as: (SEE ATTACHMENT FOR EQUATION) a) What is the probability for finding the particle in the ground state at t = 0? b) What is the probability of finding the particle between x = 0 to x = al2 a

Transverse Waves Traveling on a String and Standing Waves

Two transverse waves traveling on a string combine to a standing wave. The displacements for the traveling waves are Y1(x,t) =0.0160 sin (1.30m^-1 x - 2.50 s^-1t +.30). Y2(x,t) = .0160 sin (1.30m^-1 x +2.50s^-1 + .70), respectively, where x is position along the string and t is time. A. Find the location of the first antinod

Standing wave as sum of wave traveling to left and right

See attached file for full problem description. 9.2 Show that the standing wave f(z,t) = Asin(kz)cos(kvt) satisfies the wave equation, and express it as the sum of a wave travelling to the left and a wave traveling to the right as shown in the following equation: F(z,t) = g(z -vt) + h(z + vt)

show that functions satisfty the wave equation

See attached file for full problem description. By explict differentiation, check that the functions f1, f2 below satisfy the wave equation. Shwo that f4 does not. f1(z, t) = Ae^(-b(z-vt)^2) f2(z, t) = Asin[b(z -vt)] f4(z, t) = Ae^(-b(bz^2 + vt))

Commutator of Wave Function

Find the commutator of [x , d/dx ] for the wave function described in the attachment. See attached file for full problem description.

Calculations with Wave Functions

1.) A particle of mass m is confined to a one-dimensional potential well with infinite potential walls. The well extends from 0 (less than or equal to) x (less than or equal to) a. At time t = 0, the normalized wavefunction is (see attached file for equation) What is the wavefunction at a later time t = t0? See atta

Quantum Mechanics Question

The Hamiltonian of a certain three level system is represented by the matrix. See attached file for full problem description.

Ground State of Harmonic Oscillator

In the ground state of the harmonic oscillator, what is the probability (correct to three significant digits) of finding the particle outside the classically allowed region? (Hint: what are the minimum and maximum values of the coordinates of the respective classical oscillator with a given energy E?) Look in math tables under "

Energy StD in a Superposition of Two Stationary States

Calculate the standard deviation of the energy for a particle in a state, which is a superposition of two stationary states with coefficients c1 and c2. Do this calculation in two ways: (i) using the wave function of this state and a standard deviation of quantum mechanical averages, and (ii) using the probabilistic interpret

A particle moving in a delta potential with positive energy

A particle of mass m, with energy E>0, is moving in the potential V(x)=g[delta(x+a) + delta(x-a)] Assuming that the particle is incident from the left, what is the solution of the Schrodinger equation in all three regions (x<a, -a<x<a, x>a) for this situation? Also, what are the appropriate continuity conditions at x=+a and

Relative states and Hidden Variables in Quantum Mechanics

I ONLY NEED HELP WITH NUMBER ONE. It looks really long but the beginning is just a set up to the question. Skip to 'Your job' to see the question. I don't understand this stuff at all so if you could guide me through this step by step it would be appreciated. Explanations are important.

1-D Quantum Mechanics

A basic model of a hydrogen atom is a finite potential well with rectangular edges. A more realistic model of a hydrogen atom, although still a 1-Dimensional model, would be the electron + proton potential energy in one dimension: U(x) = -e^2/(4pi epsilon_0)|x|) a) Draw a graph of U(x) versus x. Center your graph at x = 0

Wave Functions with Uncertainty

The Wave function of a particle is seen in the attachment. a) Assuming that this function is continuous, what can you conclude about the relationship between b and c? b) Draw graphs of the wave function and the probability density over the interval -2mm <= x <= 2mm. c) What is the probability that the particle will be

Transverse Wave Properties

A uniform rope of mass m and length L hangs from a ceiling. (a) Show that the speed of a transverse wave in the rope is a function of y, the distance from the lower end, and is given by v = Sqrt(gy). (b) Show that the time it takes a transverse wave to travel the length of the rope is given by t = 2sqrt(L/g). (Hint: calculat

Mean position in a 1-D harmonic oscillator

Obtain the mean position, <x>, for a particle moving in a 1-D harmonic oscillator potential, when the particle is in the state with normalized wavefunction: Y(x)= ((a/(4*pi))^.25)*(2ax^2-1)*exp((-ax^2)/2)

Commutation relations and the uncertainty principle: normalized wave function

View the attached file for proper formatting of formulas. Consider two hermitian operators A and B which satisfy the following commutation relation: [A, B] = AB-BA=iC, where C is also a hermitian operator in general. Let us introduce a new operator Q defined by: Q=A+ i&#955;B, with &#955; being a real number, and consider

Wave Function: A Linearly Polarized Wave

Please give a step by step solution: 1) The wave function for a linearly polorized wave on a taut string is: y(x,y)=Asin(wt - kx + phi) where A =0.4m, w=3.2s^-1, k=8.1m^-1, phi = 0.49, t is in seconds and x and y are in meters. What is the speed of the wave in m/s? b) What is the vertical displacement of the string

Question about Nodes of a Standing Wave

(See attached file for full problem description) --- Nodes of a Standing Wave (Cosine) Learning Goal: To understand the concept of nodes of a standing wave. The nodes of a standing wave are points where the displacement of the wave is zero at all times. Nodes are important for matching boundary conditions, for example that