State Definition and 1000 Threads

Hello readers, Given the potential V(x) = - 1/ sqrt(1+x^2) I have found numerically 12 negative energy solutions Now I want to try to solve for these using matrix mechanics I know the matrix form of the harmonic oscillator operators X_ho, P_ho. I believe I need to perform the...

Homework Statement The Hamiltonian of helium can be expressed as the sum of two hydrogen Hamiltonians and that of the Coulomb interaction of two electrons. \hat H = \hat H_1 + \hat H_2 + \hat H_{1,2} The wave function for parahelium (spin = 0) is \psi(1,2) = \psi_S(r_1, r_2)\dot...

hello everyone, i am looking for a comprehensive link for the topic above as i want to do some research on various applications of x-rays in solid state physics. its a personal research but i have some materials but i still feel i need a whole lot more. Any form of help would be appreciated...

Hi there, I've just been having a little trouble with this short question from a past exam paper... Homework Statement "An atomic state has a dominant decay mode which produces an emission line of wavelength 6 \times 10^{-7} m and natural width 10^{-13} m . Estimate it's natural lifetime...

Hello, here is the problem that I have: Can you please tell me how to determine what is the sequence of the output. I can see it misses 101 and 010 and it repeats 000 and 100. I think both 101 and 010 are initial states. The answer I have for repeated sequence is 011, 111, 110, 100...

HCl(l) + H2O → H+(aq) + Cl-(aq) or is it HCl(g)+ H2O → H+(aq) + Cl-(aq) If HCL is liquid is it dil. or conc. ??

Homework Statement The problem involves a container holding a gas at high pressure. The container is opened to the environment, where the gas will cool down, producing a liquid or solid, and I want to find the work done by the gas throughout this process. Homework Equations PV^γ = constant U...

The Schrödinger equation rotates the state vector in Hilbert space continuously (i.e. without jumps). This makes sense for individual systems, but I'm finding this hard to reconcile with coupling or entanglement. For example, consider how Schrödinger's cat paradox is typically presented (in...

Consider a long semiconductor bar is doped uniformly with donor atoms so that the concentration is given by n = ND and is independent of position. Radiation falls upon the end of the bar at x=0, this light generates electron-hole pairs at x=0. light keeps on falling. Explanation...

Homework Statement 2N fermions of mass m are confined by the potential U(x)=1/2(k)(x2) (harmonic oscillator) What is the ground state energy of the system? Homework Equations V(x)=1/2m(ω2)(x2) The Attempt at a Solution I know the ground state energy of a simple harmonic...

Homework Statement In Kittel's 'Introduction to solid state physics' (8th ed.), on page 167, it says "The wave functions at the Brillouin zone boundary ##k=\pi/a## are ##\sqrt{2} cos (\pi x/a)## and ##\sqrt{2} sin(\pi x/a)##, normalized over unit length of line." Here I cannot understand...

I was thinking of putting together a visualization of electron orbitals as it transitions from unbounded or weakly bounded state to the ground state. However, it occurred to me that orbitals are symmetric about the proton. At some point the probability distribution must become asymmetric...

Homework Statement Find the zero input and zero state response for the following system y''(t) + 3y'(t) + 2y(t) = 2 x'(t) - x(t-1) where x(t) = (2e^-t)*u(t) U(t) is the step function Homework Equations Y = Yh + Yp Y = Yzsr + Yzir The Attempt at a Solution I can't find...

Hey. Trying to wrap my head around this maths. And given that the wave function is a superposition of a bunch of stationary states, each with a different coefficient. The coefficients squared added add to one. And the probability of finding the particle in a given state is cn^2. I know all...

Homework Statement Hello everyone! I have the following circuit to solve, and my result is a bit wrong... can you tell me please where's the mistake? E=10sin(1000t) Find the current delivered to the circuit. Find the equivalent impedance of the circuit. Find the equation of the current and...

Homework Statement The interaction between the spins of the two particles in a hydrogenic atom can be described by the interaction Hamiltonian $$\hat{H_I} = A \hat{S_1} \cdot \hat{S_2}.$$ Compute the splitting of the ground state due to ##\hat{H_I}##. Both particles have spin 1/2. Homework...

Homework Statement How to derive equation (22) on page 31 of Kittel's Intro to Solid State Physics 8th edition. The equation is: 2\vec{k}\cdot\vec{G}+G^2=0 Homework Equations The diffraction condition is given by \Delta\vec{k}=\vec{G} which from what I can surmise is the starting...

How does one construct a block diagram from the state space representation? Consider the state space: \begin{align} \dot{\mathbf{x}} &= \begin{pmatrix} 0 & 1\\ 0 & 0 \end{pmatrix} \mathbf{x}(t) + \begin{pmatrix} 0\\ 1 \end{pmatrix}\mathbf{u}(t)\\ y(t) &= x_1(t) \end{align}

Using the capacitor voltage \(v_c(t)\) and the inductor current \(i_L(t)\) as states, write the state equations for the RLC series circuit shown in the figure. We can write that \(e(t) = iR + \frac{di}{dt} + \frac{1}{C}\int i(t)dt\). I am not sure with what it wants when it says to write it...

Homework Statement This is a 3 state machine with one input variable. The input given for x produces the output sequence for z. The machine starts in state A. I am asked to derive the state table. x=010001010010010011010 A z=001000000001001000001 Homework Equations The Attempt...

State the differences between an expression and its simplified equivalent.

Hello Everyone, General curiosity question. We start with a particle who is in superposition. We observe it and collapse its wave function. This is how the particle's spin is determined. Two states can exist, spin up or spin down. My question is, once we observe the spin state, is...

Homework Statement Hi everyone, I'm having some difficulties with my code: 1. Randomly Choose a lattice at position (x, y) within the NxN lattice 2. Why by writing "int x = int(drand48()*L);" and "int y = int(drand48()*L);" it doesn't extract the value stored at that location (x, y)? 3...

Simplify 1) Simplify and state any restrictions on the variables: \frac{3a-6}{a+2} ÷ \frac{a-2}{a+2} This is what I did. Can someone tell me what I did wrong? Thanks. \frac{3a-6}{a+2} ⋅ \frac{a+2}{a-2} \frac{3a^2-12}{a^2-4} \frac{(3a+6)(a-2)}{(a+2)(a-2)} \frac{3a+6}{a+2} 3 +...

Simplify and state any restrictions on the variables: \frac{2(x+1)}{3} ⋅ \frac{x-1}{6(x+1)} This is what I did, which is wrong (according to the textbook). \frac{2}{3} ⋅ \frac{x-1}{6} \frac{2x-2}{18} \frac{2(x-1)}{18} Can someone tell me what I've done wrong? Also, how would you find the...

My textbook says the ground state energy of the QSHO is given by 1/2*h_bar*w and that this is the minimum energy consistent with the uncertainty principle. However I am having trouble deriving this myself... ΔEΔt ≥ h_bar / 2.. so then ΔE/Δfrequency ≥ h_bar / 2... ΔE*2*pi / w ≥ h_bar / 2 ΔE ≥...

I'm having some trouble with this problem: Find the volume of the solid of revolution, or state that it does not exist. The region bounded by f(x)= 6(4-x)^(-1/3) and the x-axis on the interval [0,4) is revolved avout the y-axis. How would I be able to tell whether to use the shell, disk, or...

Find the volume of the solid of revolution, or state that it does not exist. The region bounded by f(x)= the square root of ((x+3)/(x^3)) and the x-axis on the interval [1,infinity) is revolved around the x-axis. I tried using the disk method: pi* (sqrt(((x+3)/(x^3)))^2 Then I think I have to...

Homework Statement Silver has a density of 10.5E3 kg/m3 and a resistivity of 1.6E-8 Ω*m at room temperature. On the basis of the classical free electron gas model, and assuming that each silver atom contributes one electron to the electron gas, calculate the average time, Tau, between...

P.W. Anderson in his essay "more is different" said that: "no stationary state of a system has an electric dipole moment". He used an example of NH3 to illustrate that. I then checked online and found that, Chemists said there is dipole moment in NH3 molecule, but (nuclear) physicists claim...

Homework Statement Determine the system type for $$ G(s) = \frac{K}{(s + 1)(10s + 1)(20s + 1)} $$Homework Equations I am using a step, ramp, and parabolic inputs. That is, \begin{align} R(s) &= \frac{R}{s}\\ R(s) &= \frac{R}{s^2}\\ R(s) &= \frac{R}{s^3} \end{align} The Attempt at a Solution...

Supposing that some solid can exist at 2 different phases (had 2 different crystalline structure) at some temperature and pressure. Can we define the same reference entropy or chemical potential for these two states (knowing that we are talking about the same solid)?

Hi :) I'm reading a didactic paper and the author defined the initial state ket as |\Phi_{in}> = {\int}dq\phi_{in}(q)|q> where q is a coordinate and \phi_{in}(q) = <q|\Phi_{in}> = exp\left[\frac{-q^{2}}{4\Delta^{2}}\right] I don't know if I'm missing something but isn't this definition a...

f(x)= x (x+2)^2 (x-1)^4Zeros would be: 0, -2, 1 Multipicity of : 1 2 4Then for y- intercept: f(0)=0 And don't know how to graph it...

Hi, My question is partially motivated by this discussion. Suppose we have a pure state that is in a superposition for a certain basis, e.g. ##\left|\psi\right\rangle=\alpha\left| 0\right\rangle+\beta\left| 1\right\rangle##. Now a colleague of ours measures the state with respect to that...

Hi, I am designing a system to run a certain sequence when the control input is off, and then run a different sequence when the control input is on. When drawing a state diagram, for the loop where the control input is on, can the system repeat the same state twice throughout its sequence and...

If I am trying to find the steady state coefficients of a filter, when do I know the coefficients went into the steady state? In another words, steady state means it converged to a single value or that it is bounded between values? If say it is bounded between values how would I go about...

So a coherent state in quantum mechanics is "the most classical" quantum state (A Gaussian wave packet), which satisfies the Heisenberg uncertainty relation with an equality. This allows the wave packet to travel in space in a more localized fashion (like a classical particle) because its...

Homework Statement Normalize: \Psi_1 (x,t) = N_1 \cos(\frac{\pi x}{L}) e^{-\frac{iE_1t}{\hbar}} Where N_1 and E_1 are the normalization constant and energy for the ground state of a particle in an infinite square well. Homework Equations Normalization Condition: \int_\infty^\infty P(x,t)...

What is the solution of Dirac delta function of density of sate equation below: DOS(E)=2/N ∑ ∫(1/dEj(k)/dk).δ[Ej(k)-E]dE

Homework Statement The atomic mass of Niquel is 58.7 amu (atomic mass unit), and it's density (at 90ºC) is 8.86 g/cm³. (a) Find the distance from one atom to the closest one from him.Homework Equations 1 amu = 1.66053*19⁻²⁷ The Attempt at a Solution I started by finding the number of atoms...

Homework Statement An LTI system is given in state-space form, \left( \begin{array}{cc} \dot{x_{1}} \\ \dot{x_{2}} \end{array} \right) = \left( \begin{array}{cc} -1 & 0.5 \\ 1 & 0 \end{array} \right) \left( \begin{array}{cc} x_{1} \\ x_{2} \end{array} \right) + \left( \begin{array}{cc} 0.5 \\...

Has anyone seen the derivation of \(\ddot{\mathbf{r}} = -\frac{\mu}{r^3}\mathbf{r}\) into state matrix form? If so, can they provide a link?

I have the following homework question I am working on. I am given three scattering angles: 42.8, 73.2, 89. (in degrees) without the wavelength of the light used. I am to show that these are consistent with a diamond lattice. I started with Laue's Law: delta(k) = G and according to the...

I’ve been trying to understand how having indistinguishable particles in a system changes the nature of the state space. The QM texts I have gloss over this. A typical approach is to define the symmetric and anti-symmetric kets that serve as a basis for the eigenspace containing...

What is a Standard State or Reference State of an element? Can someone please give me a simple explanation of what a standard state or reference state is? I don't quite understand the way wiki describes it which is - The standard state, also known as reference state, of an element is...

Hi, I was just wondering if anyone know of an operator, which has some realistic analogue, that would perform the following action: A|N,0> = A|0,N> Where the ket's represent two joint fock states (i.e. two joint cavities) and A is the opeator I desire. I thought that the beam...

The way I understand plasma is that is almost a gas except some of the electrons of separated from the nuclei entirely making positively charged. Is there a temperature in which Iron is by definition a gas, and not a plasma? Also, can something like a noble gas become a solid?

So in a lumped parameter system, we use the ln(Θ)=exp(-hAt/ρVc), where Θ is non-dimensional temperature. This expression has 't' i.e. time in it. So does this mean it is used only for transient problems? Also, does the Biot number Bi tell us anything about whether a problem is in...

given two system is entangled, |A>=(|0_{A}>+|1_{A}>)/√2, |B>=(|0_B{}>+|1_B{}>)/√2. entangle state |AB>what is the probability to find |0_A{}0_B{}> and |1_A{}1_B{}>. are there still 1/2 just like normal inner product formulation?