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------=_NextPart_01C62B11.112A2190 Content-Location: file:///C:/A53256B1/Physics222SHOpart1_files/master18.xml Content-Transfer-Encoding: quoted-printable Content-Type: text/xml; charset="utf-8" ------=_NextPart_01C62B11.112A2190 Content-Location: file:///C:/A53256B1/Physics222SHOpart1_files/pres.xml Content-Transfer-Encoding: quoted-printable Content-Type: text/xml; charset="utf-8" ------=_NextPart_01C62B11.112A2190 Content-Location: file:///C:/A53256B1/Physics222SHOpart1_files/slide0002.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Physics 222
Physics 222
Harmonic Oscillators Part 1
(c) D.S. Durfee
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The Simple Harmonic Oscillator
nAlmost any pot= ential can be approximated by a SHO.
<= span style=3D'font-size:88%'>nClassically, t= he oscillation frequency (and period) are independent of amplitude.
<= span style=3D'font-size:88%'>nHow do we find= the allowed energys and energy eigenstates?
<= span style=3D'font-size:88%'>n     Plug potential = into TISE and solve for
        = ;  eigenstates
n     Boundary condit= ions give us an energy for
        = ;  each eigenstate.
n
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What Do the Stationary States of the Simple Harmonic Oscillator Look Like?
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What Do the Stationary States of the Simple Harmonic Oscillator Look Like?
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What Do the Stationary States of the Simple Harmonic Oscillator Look Like?
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= n=3D50 Wave Function and the Corresp= ondence Principle
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Displacing the Ground State
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charset="us-ascii" Physics 222
Displacing the Ground State
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Thought Question
nWhat will happen to the wave function after I displace it?
n
nA: It will not change with time, just sit there frozen
nB: It will simply slosh back and forth
nC: It will spread out, with the center of the wave not moving
nD: It will spread out, with the center of the wave sloshing back and forth
nE: None of the above
n
------=_NextPart_01C62B11.112A2190 Content-Location: file:///C:/A53256B1/Physics222SHOpart1_files/slide0012.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Physics 222
Evolution of P(x) for Localized “= Stationary” Particle in a Box
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