Shō Hashi (尚巴志, 1372 – June 1, 1439) was the last King of Chūzan and the first king of the Ryukyu Kingdom, uniting the three polities of Chūzan, Hokuzan, and Nanzan by conquest and ending the Sanzan period.
I'm doing a personal experiment where I take a conical spring (that is, a spring with two different diameters on either end), hang it from the ceiling, and measure the period of oscillation for different masses hanging below the spring. I do this for two different orientations of the spring; one...
At the point where we 'guess' a solution to this 2nd order ODE that cannot be done analytically, I was wondering why Griff and others choose $$e^{-x^2 / 2}$$ rather than just $$e^{-x^2}$$ I've plotted both here and am left wondering what's so different? If we guessed instead the unpopular...
Let's say I have a charge q which is viewed from its rest frame. So it's velocity v is 0. So the so-called magnetic component of its Lorentz force, which is q v x B, is 0. But I can have a magnet moving in this frame of reference.
Let's say the velocity of this magnet according to the charge's...
When I induce magnetic flux through a closed loop, I should expect the lines of flux produced by current in that loop to oppose the change of flux through that loop. But what happens when that loop, say a rectangular loop, is curved into the shape of the letter J (like a candy cane) and my flux...
What happens if I have a permanent magnet outside an ideal solenoid? Does the permanent magnet rotate until the system reaches an energy minimum in its magnetic fields? Or does the permanent magnet fail to rotate because the magnetic field of the solenoid does not reach the magnet? Wouldn't...
I am trying to perform the operation a on a translated Gaussian, ie. the ground state of the simple harmonic oscillator (for which the ground state eigenfunction is e^-((x/xNot)^2). First, I was able to confirm just fine that a acting on phi-ground(x) = 0. But when translating by xNot, so a...
Hi,
What is the physical meaning of zero probability of finding a particle in the square of the Quantum SHO wave function?
the particle is supposed to oscillate about the equilibrium position, how would it go from an end point to the other end point without passing by certain points?
Could the...
So we have derived that for the differential equation:
##x(t)''+x(t)=\delta(t)##
The solution is given by ##x=sin(t)H(t)## where ##H## is the Heaviside function.
To find this we assumed that the system was in rest before ##t=0## and that position and velocity are continious.
QUESTION: I am...
There is a post about the same problem here: https://www.physicsforums.com/threads/damped-oscilating-spring.12838/
It was helpful for solving part B.
1. Homework Statement
A 10.6kg object oscillates at the end of a vertical spring that has a spring constant of 2.05x10^4 N/m. The effect of...
I am confused about the following; where am I going wrong here?
1. (1/2)kT is defined as the average kinetic energy of the molecules of a substance at temperature T, right?
2. You can derive the Boltzmann distribution/Boltzmann factors using (1/2)kT as the kinetic energy, making an argument...
Homework Statement
Write a program to simulate motion of simple harmonic oscillator.
Initial conditions: Let ω = 1, x(t=0) = 1, v(t=0) = 0.
Integrate over 30 seconds in intervals of 0.05s.
Homework Equations
δ2x / δt2 = -ω2x
As set of 2 coupled ODE's; x' = v, v' = -w2x
The...
Spontaneous symmetry breaking refers to the solution of a system loses some symmetry in its Lagrangian. Consider a Simple Harmonic Oscillator, its lagrangian is time translationally invariant but its solution is periodic in time, thus not time-translational invariant. Is this Spontaneous...
this is the given:
the problem is the middle term, if the h-bar w outside the set brackets is canceled with the h-bar w of the m/2hw, then there will be a h-bar w that is left introduced from the middle term, i.e.
i\frac{w}{m}XP- i\frac{w}{m}PX = i\frac{w}{m}[X,P]= i\frac{w}{m}i\hbar
but...
hi, I need some reading materials on green function for SHO. my instructor provided a GF frequency and wanted us to find the deformation of poles , boundary conditions for the function. I need to know which mathematical background should I have to solve this. any useful material suggestion will...
I have just learned the quantum harmonic oscillator
When we start to Solve the schodinger equation. y"= (K - x^2) y
We look at large x behaviour and use a substitution y = u(x)* exp(-x^2 /2)
to approximate the large x behaviour first,
then we use series method to solve the equation...
when Schrodinger equation is applied to SHO only positive value of potential energy changes it to Hermitian polynomial and hence solution is possible but potential energy is positive only when the particle is moving away from the the mean position.The sign of potential is negative when the...
Hello,
I am currently studying ladder operator for a simple harmonic operator as a method for generating the energy values. This seem like a simple algebra question I am asking so I do apologize but I just can't figure it out. Here are my operator definitions...
Suppose the particle is at distance x from mean position and moving away . The standard formula for calculating potential U is U=-w here wis the work w=kxdx when the particle is moving away .On integration U=1/2Kx^2 . When the particle is moving towards mean position w=-kxdx on integration...
Homework Statement
For the SHO, find these commutators to their simplest form:
[a_{-}, a_{-}a_{+}]
[a_{+},a_{-}a_{+}]
[x,H]
[p,H]
Homework Equations
The Attempt at a Solution
I though this would be an easy problem but I am stuck on the first two parts. Here's what I did at first...
In Griffith's derivation of the quantum SHO, he uses some funny math:
first he considers asymptotic behavior to get ψ=Ae-(ε^2/2)
then he 'peels off the exponential part' to say that ψ=h(ε)e-(ε^2/2)
then he hopes that h(ε) will have simpler form than ψ(ε)
I can kind of understand the first...
Homework Statement
Ideal gas. In an ideal-gas model. N molecules move almost indepdently with very weak interactions between, in a three-dimensional box of volume V. Find the heat capacity of the system.
SHO. Consider N independent SHOs in a system. each osciallating about a fixed point...
Lets say we have two spin 0 particles that don't interact more than being indistingishable..
what are the degenercies for the energylevels?
I would say:
(n1, n2) D
---------------------------------------
(0,0) 1...
For a simple harmonic oscillator, the creation and annihilation operators can be expressed as linear combinations of the position and momentum operators,
\hat {a} = \sqrt { \frac {m \omega} {2 \hbar} } ( \hat {x} + \frac {i \hat {p} } { m \omega } )
\hat {a} ^{\dagger} = \sqrt...
Homework Statement Consider a rectangular container, dimensions L x b, filled to level h with water. Water sloshes at low amplitude, y0 << h so that its surface remains always flat. Assuming the water has a density of δ, show that the potential energy is
U(y) = \frac{1}{6} b δ g L y^2...
is it possible to derive exact values of energies of rigid rotator and SHO without using Schrodinger equation ?Is it possible to derive energy values by using classical mechanics ?
Homework Statement
I believe I understand the problem except I cannot get
the time average of [sin(wt-d)]^2 = ½
I can do the rest once this is established.
Homework Equations
Average of a function= <function>= 1/(period)* integral(f*dt) from 0 to the period
Function to be...
Homework Statement
You have a horizontal spring system such that it undergoes SHO on a frictionless surface. with a known mass attached at the end of the spring. When that mass reaches its maximum position (amplitude) a second identical mass is dropped on top of the initial, effectively...
Following Griffiths derivation on pg 44 of the eigen-states of SHO Hamiltonian, he says that we can now find all eigenvalues, but doesn't say how he knows that a and a dagger will indeed take you between nearest neighboring orthogonal states.
in other words, how do we know the ladder...
Homework Statement
The potential of a simple harmonic oscillator of HF has the following form
\frac{1}{2}kx^2 + bx^3 + cx^4
The first part of the problem involved finding expressions for the first-order energy corrections for the first three states, which I found below. Basically the x3 term...
Homework Statement
A H2 molecule can be approximated by a simple harmonic oscillator having spring constant k = 1.1*10^3 N/m. Find a() the energy levels, and (b) the possible wavelengths of photons emitted when the H2 molecule decays from the third excited state eventually to the ground...
Homework Statement
A block attached to a spring is experiencing simple harmonic motion. You know the value of postion, velocity, and acceleration at an unknown time. Find the period of oscillation, the mass of the block, and the amplitude of oscillation.
We were given values for k, x, v, a...
Homework Statement
A body of uniform cross-sectional area A and mass density \rho floats in a liquid of density \rho_0 (where \rho < \rho_0), and at equilibrium displaces a volume V. Making use of Archimedes principle (that the buoyancy force actign on a partially submerged body is equal to...
Homework Statement
A two-dimensional harmonic oscillator is described by a potential of the form
V(x,y) = 1/2 m \omega^{2}(x^{2}+y^{2} + \alpha (x-y)^{2}
where \alpha is a positive constant. Homework Equations
Find the ground-state energy of the oscillatorThe Attempt at a Solution
I have tried...
Homework Statement [/U]
The average energy of a gas of quantum SHO is
Eav= \sum_{n=0}^{\infty}n\hbar\omega e^(-n\hbar\omega/kT)\div \sum_{n=0}^{\infty}e^(-n\hbar\omega/kT)
can be solved to be
Eav=\hbar\omega\div \left \{ e^\left ( \hbar\omega/kt \right ) \right \}-1
make use of the following...
The Hermite Polynomials are solutions to the Schrödinger equation for the Quantum Simple Harmonic Oscillator. But the Hermite Polynomials are real, not complex. I thought that solutions to the Schrödinger equation always had to be complex. What am I not understanding? Thanks in advance.
Homework Statement
Two identical non-interacting spin 1/2 particles are in the one-dimensional simple harmonic oscillator potential V(x) = kx2/2. The particles are in the lowest-energy triplet state.
a. Write down the normalized space part of the wave function.
b. Calculate the energy of...
Homework Statement
I have a charged particle in a 1D harmonic oscillator, on which an externally applied electric field acts, such that the Hamiltonian can be written:
\frac{p^2}{2m}+\frac{kx^2}{2}-qEx
The problem asks to first find the first (trivial) and second order corrections to...
Homework Statement
the energy levels of a particle mass in a symmetric 3d SHO potential are:
E = (nx + ny + nz + 3/2)*h-bar*\sqrt{\frac{C}{m}}
C=constant
n=principal quantum number = nx + ny + nz
A) If 10 electrons are in the potential what's the lowest possible value for the total energy...
I know how to do SHO propagator by computing the action. I was only trying to do it
via the eigenfunction expansion
K(x’,x;t)=sum_ i phi_i(x’) phi_i(x) exp(-iε_it/hbar )=(m omega/pi*hbar)
sum_i=-^infty h_i(y’) h_i(y) exp[-(y**2+y’**2)/2] [s(t)/2]**i
with s(t)=exp(-iomega t)
This...
Quantum - Projection Probability - "Projection amplitudes for SHO states."
Given the two normalized 2D SHO wave functions <x,y|mx[/SUB ],ny> for the second energy level n = nx + ny = 1 in the m[SUB]x[/SUB ],n[SUB]y representation:
<x,y|1,0> = (2/pi)1/2xexp[-(x2+y2)/2]
<x,y|0,1> =...
Homework Statement
A horizontal massless spring of spring constant k is attached to a immovable wall at one end and a mass of 0.45kg at the other end. The spring which was not originally under tension, is now extended by 0.18 m by pulling the mass horizontally. The mass was then released by...
SOLVED: Squeeze state in quantum SHO, uncertainty
Homework Statement
So we're working with what are called squeeze states defined as |nu> = S(nu)|0> where nu is a real number, |0> the ground state of the oscillator, and S(nu) = exp[nu(a^2 - a*^2)/2] with a* = hermitian conjugate of a...
[SOLVED] Constant force perturbation of the quantum SHO
Homework Statement
We're supposed to consider the Hamiltonian for the simple harmonic oscillator:
\hat{H}_{0} = \hat{p}^{2}/2m + m\omega^2\hat{x}^2/2
With a perturbation, so that \hat{H} = \hat{H}_0 + \hat{H}' , where \hat{H}' =...
Homework Statement
My QM book says that the standard SHO potential is m \omega^2 x^2/2 . Can someone give me an example of a physical situation that is governed by this potential. It seems rather out of nowhere to me...
Homework Equations
The Attempt at a Solution
We know the eigenvalue relation for the Hamiltonian of a SHO (in QM) though relating the raising and lowering operators we get:
H= \hbar \omega (N+1/2)
This is true for H=\frac{p^2}{2m}+\frac{m \omega^2 x^2}{2}
I would like to solve for another case where V=a\frac{m \omega^2 x^2}{2}
where...
A Quantum I problem set asks me to graph the first 15 states of the simple harmonic oscillator. Our department uses mathcad heavily, so I think I should write a function that applies the ladder operator repeatedly to generate the wave function. I'm having trouble getting it to actually return a...
The even solutions of an SHO are:
h^+(y) = \sum_{s = 0}^{\infty}a_s y^{2s}
where a is given by the recursion
a_{s+1} = a_s \left( \frac{4s + 1 - \epsilon}{2(s+1)(2s+1)} \right)
The solutions are square integrable iff
a_n = 0 so that the polynomial is finite.
What I do not...
Hi all
I was just looking through my notes from my first year of my degree, and I couldn't find a missing bit. I know that Planck's postulate states that the allowed energies of a quantum simple harmonic oscillator are 0, hf, 2hf etc and that by the Schroedinger equation, you get E(n)=(n+1/2)...
This one is killing me.
Homework Statement
A SHO is resting on a horizontal surface with which it has static and
kinetic friction coefficients us and uk . We have k for the spring constant
and m for the mass. The surface is actually part of a conveyor belt
that is maintained at a speed u...