Shortest Distance Between Points-Quantum Physics-Sloved Assignment Problems, Exercises of Quantum Physics

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2.1 iF we exTtTeonmb Ths 1DoA OF THES SHORTS ST DISTANCE BETWEEN Two POINTS INA PLANE , WE CAND WRITE THE DIFFERENTIAL ELEMENT OF DISTANCE AS as = Jax? + dy? 4 of a * THE TOTAL LENGTH THEN OF A CURVE GOING FEOM P To P, WOVLD "THEN BE t- \< : | (ayy ax F x THIS EXPRESSION RESULTS IN TWO EQUATIONS OF “THE FoR mK —_— a oad +(4.,4,,%) 4% x \& “Wwe APPLY THE EULEK- LAGRANGE CAVUATION To TrHese We OBTAIN ot ~ a ot = a + (3). (<3) , ot = © Sy ax 4 ax dx cx dx AND | at ap a (8) . ah a (He) + (SE) | Fhe o yo ox ye dx AN ax * OR, = AMITD [——— ——— a fo i yi a 1 + ,@ +2: . 50 IF WE Divipe THE Fiest CF THESE EQUATIONS BY THE SECOND WE OBTHIN Yo. Oe ew ——_ 2! Az b Whee SHIELDS THE StTRarguet LIne SQUATION 4 - fare , PROCEEDING SIMILA@LY FOR THE GTHER “Two CASES WOULID Ye Liy> 4 = Bey et OL ANE “Ros ae ye et CL b, : OB WRiCw IS A Staiger UNE ANY Wart WOU Loox AT VT, docsity.com