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    Wavefunction

    A wave function describes a quantum state of particles and how they behave. The laws of quantum mechanics describe how the wave function changes over time.

    The common system for a wave function is Ѱ. Although Ѱ is a complex number, |Ѱ|² is a real number and corresponds to the probability density of finding a particle in a given place at a given time. The SI units for the wave function depend on the system. For one particle in three dimensions the units are m-3/2. The units are required so that an integral of |Ѱ|2 over a region of three-dimensional space is a unitless probability.

    The wave function is central to quantum mechanics. It is the fundamental postulate of quantum mechanics. The wave function is a source of the mysterious consequences and philosophical difficulties in the interpretations of quantum mechanics. These topics continue to be in debate today.

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    Free Particles: Wavefunction, Momentum, and Probability

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    Fourier transform with complex conjugate

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    Dimensional Harmonic Oscillator

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    Bound-state wave functions

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    One dimensional infinite square, particle with mass

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    A Spin 1/2 Particle

    A spin 1/2 particle is in the state |Psi> = Sqrt[2/3] | Up > + Sqrt[1/3] | Down > Suppose a measurement is made of the spin in the z direction and the result is m_s = -1/2. Now a second measurement is made to determine the spin in the x - direction. What is the probability the spin will be in the +x direction? So I underst

    The momentum wave function for the hydrogen atom

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    Fourier Expansion

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    Expected value of momentum and Fourier transform

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    Momentum Representation, Momentum Space Wave Function

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    Problems Involving the Schrodinger Equation

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    Two Problems in Modern Physics..

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    Problem in Quantum Mechanical Tunneling

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    Eigenvalues and Hamiltonian H

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    Eigenfunction Decomposition of 1DHO Wavefunctions

    A particle of mass m is subject to the one-dimensional harmonic oscillator potential. Write down the first three normalised eigenfunctions ?_n (x) and the corresponding eigenvalues. Initially the wavefunction is in a mixed state of the form ?(x)=(1/(7???))^(1?2) e^(-x^2/(2?)^2 ) ((3x)^2/(?)^2 +(x/?)-(3/2)+?2) where ?=?(??m?).

    2D Quantum Mechanical Harmonic Oscillator

    A particle of mass m moves in two dimensions under the influence of the potential V(x,y)=1/2 m?^2 (((6x)^2)-2xy+(6y)^2 ). Using the rotated coordinates u=(x+y)/?2 and w=(x-y)/?2 show that the Schrödinger equation in the new coordinates (u,w) is -(?^2)/2m ((d^2/du^2) +(d^2/dw^2))?(u,w)+V ?(u,w)?(u,w)=E?(u,w) Where V ?(u,w) sho

    Tunneling Probability of an Electron in a Square Well

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    Density of States Problem

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    Nano Wire Problem

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    Particle Moving in One Dimension

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    Calculating the values of Spin Angular Momentum

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    Oscillation of pendulum, inertia, amplitude, wave speed

    See attached file for proper format. 6. A physical pendulum consists of a uniform rod of mass M and length L. The pendulum is pivoted at a point that is a distance x from the center of the rod, so the period for oscillation of the pendulum depends on x: T(x). (a) What value of x gives the maximum value for T? (Use any va

    Triplet/singlet split due to perturbation

    Two identical spin-1/2 particles are confined to an infinite one-dimensional square well of width a with infinite potential barriers at x=0 and x=a. The potential is V(x)=0 for 0 <= x <= a. Suppose that the particles interact weakly by the potential V_1(x)=Kdelta(x_1 - x_2), where x_1 and x_2 are the positions of the two particl

    Quantum Mechanics: Time dependent perturbation problem

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    Time Dependent Perturbation

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