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
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
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)
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+ iλB, with λ being a real number, and consider
Semi-infinite potential: Derivation of the transcendental equation for the case of E < Vo and finding the reflection coefficient for the case of E > Vo
A semi-infinite potential well is given as shown in the figure. ---------- Figure ------------------- (a) Consider the case when (0<E<Vo).Show the quantization of energy is given by the following transcendental equation: --------Equation -------------------- (b) A particle of energy E> Vo is incident from the rig
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
(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
Find the lesser and greater values of the radius where the n = 2, l = 0 radial probability density has its maximum values.
Find the equation of motion for a particle at x=6.1 for a transverse sine wave with frequency 208 Hz and amplitude .233 meters if the wave propagates in the x directon at 68 m.s, provided the particle at x=0 has equation of motion y=A sin('omega t).
Write an expression for a harmonic wave that has a wavelength of 2.8 m and propagates to the left with a speed of 13.3 m/s. The amplitude of the wave is 0.12 m.
(a) Use this reursion formula, c_j+1 = (2(j+l+1-n)*c_j)/((j+1)(j+2l+2)), to confirm that when l=n-1 the radial wave function takes the form: R_n,n-1 = (N_n)*r^(n-1)*e^(-r/(na)) (b) Calculate <r> and <r^2> for states psi_n,n-1,m.
If a hydrogen atom is in the ground state, what is the probaility of finding the electron in a volume of 1.0 pm^3 at a distance of 52.9 pm from the nucleus, in a fixed but arbitrary direction? 1 pm = 10^-12 m
I am given three unnormalized wavefunctions for the system: psi(x) = 100e^x for x<-4 psi(x) = 0.73 cos[(pi)x/40] for-4<x<4 psi(x) = 100e^-x for x>4 I need to determine the probability of the wavefunction vs. x for this system from x=-10 to x=10 so that I can plot it. I have to comment on the probability of fin
Please, show me how you got the answers and give me the answers. Please choose the answers from the chose Thanks
1. A 100-keV x ray is Compton-scattered through an angle of 90 degrees. What is the energy of the x ray after scattering? a. 83.6 keV b. 121 keV c. 114.5 keV d. 100 keV 2. What is the de Broglie wavelength of a particle moving at a speed of 1.00 x 10^6 m/s if it is (a) an electron (b) a proton? (me= 9.11
Derive the infinite square well energy quantization law, directly from the DeBroglie relation p=h/l, by fitting an integral number of half DeBroglie wavelengths l/2 into the width a of the well
Suppose that a pair of electrons, A and B, were described by the following wave function: (see attached for equations). (I have rewritten this equation as I believe some of you are having problems reading the text.) What property specific to entanglement must the wavefunction describing an entangled state of two particles
A 3kg particle has a velocity of (3i-4j) m/s. Find the magnitude of its momentum? ============================================= Answers: a) 9kg m/s b) -12 kg m/s c) 15 kg m/s d) 3 kg m/s ################################################## A sinusoidal wave is described by y=(0.30m)sin(0.20x-40t). Determine the wave speed.
Wavefunctions of a finite square well. See attachments for details.
The schroedinger equation for harmonic oscillator can be written: E*psi = [(h^2)/2m][((d^2)*psi)/(dx^2)] + (1/2)kx^(2*psi) Write and formally differentiate each term to get the second derivative with respect to X. Put it all into the equation as shown and you will see that there will be an infinite number of possible solu
Two identical, non-interacting spin-1/2 fermions are placed in the 1-D harmonic potential V(x) = (1/2)m ω2x2, Where m is the mass of the fermion and ω is its angular frequency. a. Find the energies of the ground and first excited states of this two-fermion system. Express the eigenstates corresponding to these two
See attached file. A traveling wave on a wire is expressed by the equation: (1) y= .24 sin (11x - 16t). Distances are in meters, times in seconds. PART a. On a general sine curve that you see in ATTACHMENT #1, Show a properly located y axis for the graph of y(x) at t= .25 sec. Calculate and label the y intercept and thr