Transmission coefficients of a 1D particle in delta potentials
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4. A particle of mass m, with energy E>0, is moving in the potential
V(x) = g
a. Write down the solution of the Schrodinger equation in all three regions (x
Problem #1
Consider the Gaussian Distribution ρ(x)= Ae^(-λ(x-a)^2), where A, a, and λ are positive real constants (Look up any integral needed)
[A] Use equation 1= ∫ ρ(x) dx (limits on integral are negative infinity to positive infinity) to determine A.
[B] Find
(See attached file for full problem description)
(See attached file for full problem description)
Calculate the standard deviation of the energy for a particle in a state, which is a superposition of two stationary states with coefficients c1 and c2. Do this calculation in two ways: (i) using the wave function of this state and a standard deviation of quantum mechanical averages, and (ii) using the probabilistic interpret ...continues
Time evolution of the wavefunction of a particle in a square well
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Quantum probability, probability current, commutators
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In the ground state of the harmonic oscillator, what is the probability (correct to three significant digits) of finding the particle outside the classically allowed region? (Hint: what are the minimum and maximum values of the coordinates of the respective classical oscillator with a given energy E?) Look in math tables under “ ...continues
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