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    Particle in a box ground states

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    The ground state wave function for a particle in a box confined to a 1-D box of length L is Ψ=(2/L)^(1/2) sin (pi x/ L)
    Suppose that the box is 10.0 nm long. Calculate the probability that the particle is
    a) between x=9.90 nm and x= 10.0 nm
    b) in the right half of the box

    © BrainMass Inc. brainmass.com December 24, 2021, 8:41 pm ad1c9bdddf
    https://brainmass.com/physics/wavefunction/particle-box-ground-states-302022

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    We start with the simple trigonometric identity:
    (1.1)
    Therefore:
    (1.2)
    The probability to find the particle between and is given by:
    (1.3)
    For the ground state:
    (1.4)
    Therefore:
    (1.5)
    Simple substitution:
    (1.6)
    And we get normalization of the box width (we set L=1) and the interval is now measured in the fraction of the box's size
    (1.7)

    For we obtain the probability:

    For we obtain the probability:

    As expected, due to the symmetry of the ground state the particle has 50% to be in the right 50% of the box.

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    © BrainMass Inc. brainmass.com December 24, 2021, 8:41 pm ad1c9bdddf>
    https://brainmass.com/physics/wavefunction/particle-box-ground-states-302022

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