The Schrӧdinger Equation

Find the expectation value of the square of the momentum squared for the particle in the state, \(\Psi(x, t)=A e^{i(k x-\omega t)}\). What conclusion can you draw from your solution?

Text Transcription

Psi=Ae^i(kx-omega t)

• Physicsisanexperimentalscience o Performobservationsofnaturalworld o Makeexplanationsforitspropertiesandbehaviors o Expresstheseexplanationsmathematically o Testandrefineexplanations 1) Theuniversebehavespredictably 2) TheScientificMethod OBSERVATION FINDAPATTERN BUILDONHYPOTHESIS DEVELOPAHYPOTHESIS YES WASTHEPREDICTION RIGHTORWRONG MAKEATESTABLE PREDICTION NO DOTHETEST REVISEORREJECTIT • Motionisachangeinpositionovertime o Whatisposition • ReferenceFrame o Origin–adesignated“center”spot o Coordinateaxes–designateddirections o Timezero Hypothesis Prediction • Explanationofsomesort • If…Then • Basedonanunderlyingmechanism • Conditional • Somethingyoucantest • Index:Something