The Wigner function,
W(x,p)\equiv\frac{1}{\pi\hbar}\int_{-\infty}^{\infty}
\psi^*(x+y)\psi(x-y)e^{2ipy/\hbar}\, dy\; ,
of the quantum harmonic oscillator eigenstates is given by,
W(x,p) = \frac{1}{\pi\hbar}\exp(-2\epsilon)(-1)^nL_n(4\epsilon)\; ,
where
\epsilon =...
Homework Statement
I doubt energy is conserved in SHM, or it might be possible that i be doing something wrong.
The particle (red dot) in the attachment is at its equilibrium position and oscillates with Simple Harmonic Motion between the two yellow colored plates.
Amplitude A = 1.5 m...
1. when wave is destructive interference ,where is the energy? for example, two plane wave have opposite phase ,they will destructive interference completely,but where is the energy? in antireflection film, the reflection wave is disappear!why? where is the energy? where is the wave?
2.in what...
Simple Harmonic Motion (F=-kx) -- Help!
Hello Ladies & Gentlemen please answer my question:
Q: The formula for Hooke's LAW is Felastic=-kx , so, the "X" is always negative? And the "F" is always negative? I know the "K" is always should be positive but please explain to me because I'm confused...
Homework Statement
A cheerleader waves her pom-pom in simple harmonic motion with an amplitude of .180m and a frequency of .850Hz.
a) Find the maximum magnitude of the acceleration and of the velocity.
b) Find the acceleration and speed when the pom-pom's coordinate is x=+.090m.
c)...
Homework Statement
http://www.mediafire.com/view/?7045cz9au1ci7cd
A mountain bike has bad shock absorbers (w0/γ = 10) that oscillate with a period of 0.5 seconds after hitting a bump. If the mass of the bike and rider is 80kg, determine the value
of the spring constant k (remembering that...
So my professor was discussing the case of a mass suspended from a vertical massless spring in some viscous liquid.
He arrives at the equation of motion which was :x: + \frac{b}{m}x. + \frac{k}{m}x = 0
x: is the second derivative of displacement wrt time. similarly x. is the first derivative...
Homework Statement
I have 8 pipes for a school project taped together to make a pan flute, they are 7, 9, 11, 13, 15, 17, 19, 21 inches... 1 inch diameter each one. I have to find the frequency of each one, but I'm not sure what the Harmonic numbers are. It is an open-ended instrument. I plan...
Hi all,
this is my first time on PF.
I do not know English but I have a problem of a harmonic oscillator.
I have rather large head, help me please , I do not know what else to do ...
I have this problem:
Consider the harmonic oscillator with an additional repulsive
cubic force...
In my physics class we're talking about LC and LRC circuits, and the equations are analogous to those for SHM. However, I don't see how x=Acos(ωt+\varphi) satisfies m(d^2x/dt^2)+(k/m)x=0. I've never done differential equations and in the book it seemed like the author just guessed and checked...
Homework Statement
Homework Equations
F=ma
The Attempt at a Solution
I did the first three parts . The last part of this question is quite hard, i tried using Newton's 2nd law of motion but ... here is what happens :
T is the tension, as stated in the question .
so the equation of...
Homework Statement
So you're being pushed on a swing by someone who is whistling at a constant 60Hz. At the bottom, Vmax is 4 m/s. Explain what you hear as you swing toward and away from the source of whistling (speed of sound is 343 m/s for this problem).
Homework Equations
Observed...
Homework Statement
Find the uncertainty of the kinetic energy of a quantum harmonic oscillator in the ground state, using
\left\langle p^2_x \right\rangle = \displaystyle\frac{\hbar^2}{2a^2} and
\left\langle p^4_x \right\rangle = \displaystyle\frac{3\hbar^2}{4a^2}
Homework Equations...
Homework Statement
What is the effect of the sequence of ladder operators acting on the ground eigenfunction \psi_0
Homework Equations
\hat{A}^\dagger\hat{A}\hat{A}\hat{A}^\dagger\psi_0The Attempt at a Solution
I'm not sure if I'm right but wouldn't this sequence of opperators on the ground...
Im kind of confused on which acceleration equation to use.
A = -(kx)/m
or
A = -(w^2)Acos[(angular freq)(time) + phase constant]
as both of these contribute to SHM.
Im guessing I can use the first acceleration equation when i know how far the object stretched and if i don't i...
Okay, so if a harmonic oscillator has a restoring force given by Hooke's Law such that
Fs = -kx
and its integral gives the potential energy associated with the restoring force:
PE = -(1/2)kx2
Then for the total energy of a harmonic oscillator, why is the TE:
TE = Evibration +...
Homework Statement
A mass m hanging on a spring oscillates vertically. If the equilibrium point of the oscillation is a distance d below the relaxed length of the spring and if the amplitude of the oscillation is A, what is the maximum kinetic energy of the oscillation?[b]2. Homework Equations...
I have done a handful of problems related to sound waves in air columns and one thing I have noticed is that, unless told otherwise in the problem formulation, one always assumes that sound wave that is formed is always the fundamental harmonic and thus the length of the air column comprises a...
Homework Statement
For the n = 1 harmonic oscillator wave function, find the probability p that, in an experiment which measures position, the particle will be found within a distance d = (mk)-1/4√ħ/2 of the origin. (Hint: Assume that the value of the integral α = ∫01/2 x2e-x2/2 dx is known...
Homework Statement
A 24-lb weight, attached to the end of a spring, stretches it 4 inches. Find the equation of motion if the weight is released from rest from a point 3 inches above the equilibrium position.
Homework Equations
\frac{d^{2}{x}}{dt^2}+\frac{k}{m}x=0
F=ma
The Attempt...
Hi all
Homework Statement
I have the first three states of the harmonic oscillator, and I need to know the amplitudes for the states after the potential is dropped.Homework Equations
u_{0}=(\frac{1}{\pi a^{2}})^{\frac{1}{4}} e^{{\frac{-x^2}{2a^2}}}
u_{1}=(\frac{4}{\pi})^{\frac{1}{4}}...
Problem:
In a harmonic oscillator
\left\langle V \right\rangle=\left\langle K \right\rangle=\frac{E_{0}}{2}
How does this result compare with the classical values of K and V?
Solution:
For a classical harmonic oscillator
V=1/2kx^2
K=1/2mv^2
I don't really know where to begin. Is it safe...
Homework Statement
A damped oscillator is subjected to a simple harmonic force, satisfying $$\ddot{x}(t) + 2k\dot{x}(t) + \omega^2x(t) = g \cos (nt), $$where ##g, k, \omega, n +ve.##
1) Show that for ##t >>1/k## the position x(t) has the form ##A \cos (nt - \phi)##, and find A and ##\phi##...
Homework Statement
Consider a system of N distinguishable, non-interacting harmonic oscillators. The Hamiltonian is given (shown below).
Assuming that the oscillators obey Schrodinger's equation, determine the canonical partition function for the system. Then assume the oscillators obey...
Hello! I have this general question regarding (musical) frequencies:
I'm having a bit of a hard time putting what makes logical sense to me, as opposed to what I'm being taught in school. My teacher is basically saying the following: If the fraction/division of two frequencies is rational, the...
Homework Statement
the problem and a possible solution(obtained from a book) is attached as a pdf to the post.However Iam unable to understand it.Please download the attachment.
Homework Equations
equation no (2) in the pdf.Is there any use of space translation operator in here.The Attempt at...
Homework Statement
Not exactly sure why a time value of 0.500s is given, but I am positive it is why my answer isn't correct:
Q. a 1kg object is attached to a horizontal spring. The spring is initially stretched by 0.100m and the object is released from rest there. It proceeds to move...
Homework Statement
A particl of mass m in the potential V(x) (1/2)*mω^{2}x^{2} has the initial wave function ψ(x,0) = Ae^{-αε^2}.
a) Find out A.
b) Determine the probability that E_{0} = hω/2 turns up, when a measuremen of energy is performed. Same for E_{1} = 3hω/2
c) What energy...
Homework Statement
1)Consider a particle subject to the following force ##F = 4/x^2 - 1## for x>0.
What is the particle's maximal velocity and where is it attained?
2)A particle of unit mass moves along positive x-axis under the force ##F=36/x^3 - 9/x^2##
a)Given that E<0 find the turning...
Homework Statement
Find a value for n for which the nth partial sum is ensured to approximate the sum of the alternating harmonic infinite series to three decimal places.
Homework Equations
Sn = Ʃ(-1)^k+1*1/k = 1 - 1/2 + 1/3 - 1/4 + 1/5 - . . .
S1 = 1
S2 = 1 - 1/2
S3 = 1 - 1/2 + 1/3
S4...
Homework Statement
We have U-shaped tube filled with liquid , if liquid is displaced through length 'x' find
time period of SHM
please help me :confused:
Homework Statement
A massless spring hangs down from a support, with its lower end at y=0, where the y-axis is vertical and points downward (normal orientation of y). When a small unknown mass is attached to the spring, the lower end of the spring moves down to a position y_0 for the mass...
Homework Statement
Write down the v=1 eigenfunction for the harmonic oscillator. Substitute this eigenfunction into the Schrodinger equation and show that the eigenvalue is (3/2)hν.
Homework Equations
The Attempt at a Solution
I'm not really sure on how to to this, but here's...
Homework Statement
I am unsure as to a step in Griffiths's derivation of the quantum harmonic oscillator. In particular, I am wondering how he arrived at the equations at the top of the second attached photo, from the last equation (at the bottom) of the first photo (which is the recursion...
Hi,
Consider a block of mass M connected to a spring of mass m and stiffness k horizontally on a frictionless table. We elongate the block some distance, and then release it so that it now oscillates.
According to the theoretical study using energy methods, we see that the mass of the...
Homework Statement
Dear Guys,
Does f(x,t)=exp[-i(ax+bt)^2] qualify as a harmonic waves? Please help!
Manish
Germany
Homework Equations
The Attempt at a Solution
it is of the form g(ax+bt). which is the general form for harmonic wave. but what bothers me is the...
Homework Statement
I have a ball of 20 kg describing a damped harmonic movement, ie,
m*∂^2(x)+R*∂x+K*x=0,
with m=mass, R=resistance, K=spring constant.
The initial position is x(0)=1, the initial velocity is v(0)=0.
Knowing that v(1)=0.5, v(2)=0.3, I have to calculate K and R...
So I am trying to model a harmonic oscillator floating on the oceans surface. I treated this as a harmonic oscillator within a harmonic oscillator and I am not sure if I am heading in the correct direction. Just to be clear this isn't a homework problem just something I am working on.
The...
Homework Statement
A meterstick is clamped to a tabletop. The end of the meter stick is deflected downwards a small distance x and is released such the end of the meterstick moves up and down in simple harmonic motion. The meterstick is measured to oscillate up and down 10 times in 5.0...
Homework Statement
A 100g particle hangs freely at rest on the end of a spring of stiffness 10N/m. If
the particle is projected upwards with a speed of 2m/s, find the time taken until
it first comes to rest and the distance travelled.
Homework Equations
Well, there's F = -k.x and of course the...
It isn't making any intuitive sense. If it isn't moving in circular motion, how can it have angular frequency or speed?
Also,
v=\pm ω\sqrt { A^{ 2 }-x^{ 2 } }
only applies to SHM with springs only, right?
Also, does anyone know how to derive this equation below?
x=\frac { \pm \sqrt { { { v...
Homework Statement
Find the resultant of the superpostion of two harmonic waves in the form
E=Ecos(α-ωt)
with amplitudes of 3 and 4 and phases of π/6 and π/2 respectively. Both waves have a period of 1s.
Homework Equations
ω=2πf = 2π/t
The Attempt at a Solution
I first...
Hello,
I want to include kinetic friction into the harmonic oscillator.
A small blocks is attached to a horiontal spring on a table.
Because there is kinetic friction there are two forces on the blok that we need to describe the oscillation.
First, the force that the spring exerts and second...
Homework Statement
Homework Equations
F = -dU/dx
The Attempt at a Solution
U = \frac{1}{2}kx^2 + mgxsin\theta \\\\
F = -(kx + mgsin\theta) \\\\
F = -kx - mgsin\theta \\\\
We want to set the force = 0 because that's when the block is in equilibrium with no forces acting on...