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S c s Ŋ ̃ T C N V b v ł B x r E L b Y E Ԃ E q p i E Ƌ A Ɠd A A e B N A A A L W ̃ T C N i ŊF l ̐ ܂ B I x r E q p i ܂ l ̗m 荂 ̂ Ȃ Ȃ q B f U C i ̗ǂ Ǝq ǂ ̐ ɍ 킹 ĕp ɂɔ l i ̎荠 ̃o X ŔY ނ Ƃ ܂ B. Background Schrödinger's equation Schrödinger's equation, in bra–ket notation, is = ^ where ^ is the Hamiltonian operator The Hamiltonian operator can be written ^ = ^ (^) where (^) is the potential energy, m is the mass and we have assumed for simplicity that there is only one spatial dimension q The formal solution of the equation is. A t g d k w b g J i r w E w b g p ` C J j w b g u ɂ č ` X s J ɕϐg I o C N c O E T L b g E X w b g g p ̃R ~ j P V c Ƃ Ăa t g d k w b g p ` C J p B.

CHAPTER 4 CANONICAL TRANSFORMATIONS, HAMILTONJACOBI EQUATIONS, AND ACTIONANGLE VARIABLES Let us try the transformation p= p 2mPcos(Q) (434) q=. X p c x Őh l Ɍ n i Ɂi Ɛϋɓi Ƀx p c x 𗿗 Ɏg ܂ 傤 i. T B s q 󂲗 p @ } j s i q 󌔁@< l N > o n H c ȃN X y ӎ zU ^ C v i L j q 󌔂͂ \ Ɠ ɂ w K v Ȃ ߁A ̎ z ƂȂ ܂ B.

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~ h Scom ́A S C 50,000 _ ̈ S q p i P w ł l b g ʔ̃T C g ł B g i E p J T Ȃ獑 ő K ͂̕i A ~ h Scom p B i l w Ɍ j ̑ ͖ ł j. J h w k G r L V c U c U e Z q G U r ^ O X H ` M p J L 4 X M 7 d L T e r L ` L e 7 H o J j e G V o ;. I ʈꗗ ͈ꕔ ̃ J 𔲐 Ă ܂ I ԍ A A S X ^ A S X ^ h l o n q s.

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Ae Aeƒ A Ae A A I œaes Ae ªa Ae E A A A A Ae ÿa E A Sa A Eƒ A Aeˆ Aœ E Ae Aes Ae ªc A Cº A Ae ÿa E Ae A

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A A Sa Ae Ae Se A Zaººas Eµ Aeº A œc A Sa Esœa

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Q Tbn And9gcs Vmhexu8 Qoiviakmgr7 Birmmvcu0pwil Jhclxul02yku11 Usqp Cau

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