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# Differences

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activities:guides:spqmevolution 2011/07/14 13:54 | activities:guides:spqmevolution 2018/10/18 10:03 current | ||
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Students work in groups to solve for the time dependence of two quantum particles under the influence of a Hamiltonian. Students find the time dependence of the particles' states and some measurement probabilities. | Students work in groups to solve for the time dependence of two quantum particles under the influence of a Hamiltonian. Students find the time dependence of the particles' states and some measurement probabilities. | ||

+ | |||

==== Prerequisite Knowledge ==== | ==== Prerequisite Knowledge ==== | ||

* Spin 1/2 systems | * Spin 1/2 systems | ||

* Familiarity with how to calculate measurement probabilities | * Familiarity with how to calculate measurement probabilities | ||

- | * Solutions to the Schrödinger equation | + | * Solutions to the Schrödinger equation for a time independent Hamiltonian |

* Dirac notation | * Dirac notation | ||

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* [[:Props:start#whiteboards|Tabletop Whiteboard]] with markers | * [[:Props:start#whiteboards|Tabletop Whiteboard]] with markers | ||

* A handout for each student | * A handout for each student | ||

+ | |||

==== Activity: Introduction ==== | ==== Activity: Introduction ==== | ||

- | Little introduction is needed. | + | Little introduction is needed, although you may want to review how to find a time-evolved state for a time-independent Hamiltonian. |

==== Activity: Student Conversations ==== | ==== Activity: Student Conversations ==== | ||

+ | |||

==== Activity: Wrap-up ==== | ==== Activity: Wrap-up ==== | ||

- | The main points of this activity are addressed in the last question. Students should try to see a pattern of how these calculations proceed, and should learn to recognize a stationary state. Students should also recognize that measurement probabilities of non-stationary states will be time dependent UNLESS you measure an eigenstate of the Hamiltonian. | + | The main points of this activity are addressed in the last question. Students should recognize: |

+ | * a pattern of how these calculations proceed, and should learn to recognize | ||

+ | * a stationary state | ||

+ | * that measurement probabilities of non-stationary states will be time-dependent UNLESS you measure a quantity that commutes with the Hamiltonian. | ||