Explore BrainMass

Explore BrainMass

    Schrodinger

    Schrodinger’s cat is a thought experiment devised to illustrate what Erwin Schrodinger saw was the problem of the Copenhagen interpretation of quantum mechanics applied to everyday objects. He found that there was a contradiction with common sense.

    Schrödinger’s cat presents a scenario where a cat may be both alive and dead, depending on an earlier random event. The original experiment was imaginary; however similar principles have been researched and used in practical applications. The thought experiment is often featured in theoretical discussions of the interpretations of quantum mechanics.

    Schrödinger’s thought experiment [1]

    One can even set up quite ridiculous cases. A cat is penned up in a steel chamber, along with the following device (which much be secured against direct interference by the cat): in a Geiger counter, there is a tiny bit of radioactive substance, so small that perhaps in the course of the house, one of the atoms decays, but also, with equal probability, perhaps none; if it happens, the counter tube discharges, and through a relay releases a hammer that shatters a small flask of hydrocyanic acid. If one has left this entire system to itself for an hour, one would say that the cat still lives if meanwhile no atom has decayed. The psi-function of the entire system would express this by having in it the living and dead cat mixed or smeared out in equal parts. It is typical of these cases that an indeterminacy originally restricted to the atomic domain becomes transformed into macroscopic indeterminacy which can then be resolved by direct observation. That prevents us from so naively accepting as valid a “blurred model” for representing reality. In itself, it would not embody anything unclear or contradictory. There is a difference between a shay or out-of-focus photograph and a snapshot of clouds and fog banks.
    - Erwin Schrodinger, Die gegenwartige Situation in der Quantenmechanik (The oresent situation in quantum mechanics), Naturwissenschaften

     

    [1] Schrödinger, Erwin (November 1935). "Die gegenwärtige Situation in der Quantenmechanik (The present situation in quantum mechanics)".Naturwissenschaften.

    © BrainMass Inc. brainmass.com March 28, 2024, 4:58 pm ad1c9bdddf

    BrainMass Solutions Available for Instant Download

    first-order energy correction in case of 1-D delta-function

    Recall that a 1-D delta-function potential well of the form V (x) = −B delta(x) had exactly one bound state, with a double-tailed exponential wave function. (a) Apply a harmonic oscillator perturbation of the form V ′(x) = (m omega^2 x^2)/2. Calculate the ground-state energy for this perturbed system to first order. (b)

    States probabilities

    An angular momentum system is prepared in the state |Psi> = 1/Sqrt(10) ( |1 1> - 2|1 0> + 2i|2 2> + i |2 0>) What are the possible results of a measurement of the squared angular momentum L_hat^2 and with what probabilities would the occur? Can you please show me a step by step solution for how to solve these type of qu

    First order perturbation in an infinite spherical well

    Please see attached question. Update: The correction is due to relativistic effects. -(1/2mc^2)(E^2-2E[V]+[V^2]) Where [V] is the expectation value of the potential I updated the question. Please let me know if you need more.

    Energy Levels, Eigenstates, Spin State of Particle System

    Please see attached for full question. A particle of spin 1/2 is placed into a magnetic field with a Hamiltonian of (see attachment) 1. Find the eigenvalues and eigenvectors? 2. A particle is initially prepared to be in a state .... Find x(t) 3. If you measure the z-component of the particles angular momentum, what is the

    Particle in a 3D box calculation

    5. Consider a cubic infinite potential well of length L. (Assume that the particle is confined to stay withing 0 and L in all the directions.) (a) What is the ground state energy and the ground state wavefunction? (b) What is the next energy level? Are there more than one wavefunction with the same energy? If there are then writ

    3D isotropic harmonic oscillator

    a particle of mass m and electric charge q moves in a 3D isotropic harmonic oscillator potential V=1/2kr^2 (a) what are the energy levels and their degeneracies? (b) if a uniform electic field is applied, what are the new energy levels and their degeneracies? ******(c)if a uniform magnetic field is applied, what are th

    Addition of angular momentum

    Consider a deuterium atom (composed of a nucleus of spin I = 1 and an electron). The electronic angular momentum is J = L + S, where L is the orbital angular momentum of the electron and S is its spin. The total angular momentum of the atom is F = J + I, where I is the nuclear spin. The eigenvalues of J^2 and F^2 are J(J+I)h^2

    Time Evolution of Speed

    Consider a spin 1/2 particle of magnetic moment M=yS. The spin state space is spanned by the basis of the | - > vectors, eigenvectors of S with eigenvalues + h/2 and -h/2. At time r=-, the state of the system is seen in attached file as well as questions a,b, and c. Reference: "Cohen Quantum Mechanics"

    Commutation and Completeness in 1D Hamiltonian

    I need some help with this Hamiltonian question: Consider the Hamiltonian H of a particle in a one-dimensional problem defined by: H = 1/2mp^2 + V(X) Where X and P are operators defined in E of chapter 2 and which satisfy the relation: [X, P] ih. The eigenvectors of H are denoted in the attached file, as well as the questio

    Projection Operators

    Let K be the operator defined by K = | phi> <psi |, where | phi> and | psi > are two vectors of the state space. (a) Under what conditions is K Hermitian? (b) Calculate K^2. Under what condition is K a projector? (c) Show that K can always be written in the form K=lamba*P1P2 where lamba is a constant to be calculated and P1

    Time evolution of the ladder operators

    The evolution operator U(t,0) of a one-dimensional harmonic oscillator is written: U(t,0) = e^(-iHt/h) with: H = hw(a^t*a + 1/2) Consider the operators: a(t) = U^t(t,0) a U(t,0) a^t(t) = U^t(t,0) a^t U(t,0) By calculating their action on the eigenkets | phi(n) > of H, find the expression for a(t) and a^t(t) in ter

    Time evolution of spin

    See attached file for equations and answer the following: (a) Calculate the matrix representing in the { | + >, | - > } basis, the operator H, the Hamiltonian of the system. (b) Calculate the eigenvalues and the eigenvalues of H (c) The system at the time t = 0 is in the state | _ >. What values can be found if the energy

    Derivation of Virial Theorem in Quantum Mechanics

    Solving for Virial Theorem (look at image attached for better symbol representation) a. In a one-dimensional problem, consider a particle with the Hamiltonian: H = p^2/2m + V(X) where: V(C) = lambaX^n Calculate the commutator [H, XP]. If there exists one or several stationary states |> in the potential V,

    Ehrenfest Theorem for one dimensional problems

    In a one-dimensional problem, consider a particle of potential energy V(X) = -fX, where f is a positive constant [V(X) arises, for example, from a gravity field or a uniform electric field]. a. Write Ehrenfest's theorem for the mean values of the position X and the momentum P of the particle. Integrate these equations, compare

    Ehrenfest's Theorem

    Spreading of a free wave packet: Consider a free particle a. Show, applying Enhrenfest's theorem that <X> is a linear function of time, the mean value <P> remaining constant b. Write the equations of motion for the meal values <X^2> and <XP+PX>. Integrate these equations.

    Transmission coefficient of the finite square well

    A particle of positive energy approaches the square well illustrated in fig 3.5 - attached- from the left. some of the wave will be transmitted and some will be reflected. a) calculate the transmission amplitude b) show that the transmission amplitude equals 1 when 2k'L = npi, where k'= [sq rt ((2m(E+V_0))/h-bar] is the wav

    Transmission and Reflection From a Potential Step

    Find the solution of Schrodinger equation for a particle of mass m and energy E incident from the right on the potential step shown in fig 3.14 (attached file). Compare the probability currents in the reflected wave and in the transmitted wave with the probability current in the incident wave, and deduce the probabilities of ref

    Operators and eigenvectors

    Show that operator Q can be written (Summation) q_n|q_n><q_n| An operator Q has eigenvectors |q_n>, Q|q_n> = q_n|q_n> n=1,2,3..... Suppose that these eigenvectors |q_n> form a complete set. Show that in this case the operator Q can be written Q= [(capital

    Complex Analysis: Set Theory

    I just had a confusing lecture on the following: Open Set Closed set Open and Connected Domain Bounded and Unbounded sets The lecture was confusing to say the least. Could you please give me a clear explanation of these concepts with examples? By the Way: Heisenberg and Schrodinger are in a car and are stopped by po

    Finding the Ground State Energy for Bosons and Fermions

    Consider three particles, each of mass m, moving in one dimension and bound to eachother by harmonic forces, i.e., V=k/2*[(x_1-x_2)^2+(x_2-x_3)^2+(x_3-x_1)^2] 1) Write the (time-independent) schrodinger equation for the system. 2) Transform to a new coordinate system (having the center of mass as one of the coordinates),

    Electron Configuration Characteristics

    See attachment. Compare the elements B, Al, C, and Si: (a) Which has the most metallic character? (b) Which has the largest atomic radius? (c) Which has the greatest electron affinity? (d) Place the three elements B, Al, and C in order of increasing first ionization energy. Name the element corresponding to each characte

    Help with Schrodinger's Statistical Thermodynamics Text

    I was just wanting to see the steps in between for the two highlighted equations in the attached file from Schrodinger's Statistical Thermodynamics text. I just cannot seem to come up with the same 2nd equation in my calculations. Thank you very much! (the 'log' in the text is actually 'ln' or log base e) ** Please see the at

    Applying Schrodinger's Equation

    Suppose the V(x) is complex. Obtain an expression for the equation in the file (see attachment). For absorption of particles the last quantity must be negative (since particles disappear, the probability of there being any decreases). What does this tell us about the imaginary part of V(x)?