Question

(( 8)) In each case show that F(x) is an eigen-function of the operator and find the eigen-value F(x) Eigen-value i) d/dx? cos ax ii) d/dt elat iii) d/dx2 + 2d/dx + 3 ex iv) d/dy xey v) V2 - d/dx2 + d´/dy2 + d´/dz2 cos ax cos by cos cz

Answer 1

An on opentalor quaslüm morhanie an operator furformed certain wave bunction and erotwins with the rear of unchas value and that value is called regen values. Apa ya ware finchon nator eigen walne a cos (ax) À Fla) s Cansan) ( (cmx)) Elena C - ash (ax)) E-a venit sin (02)) -a.a cos ax = -a coslan) À F() -a? Cos(an). © în I ar Eigen value = (-a); fa cinta denna Iliad a incial ia fm) Eigen value = tai] et (2^x) = aega. - 14.217). g. (021). ange": g'dan * bo po co za gente com] : n't" *r sent I so can[ aita+3] Scanned with CamScanner Egen value = ata +3 (1

dy : sence we will be differentialing wanit to y so a romponent will be constant. F(X) = zeby pre Ergen value um per + d2 te d22 + Q2 FCA) = cosaz.cos by cas f(a) = cos arcos by Case the general cosaa) a daz da cosaxla nina - real ca sin ax) = -a & (sinax) = -a, le cos ax cos by cos cz)) , = cos by cosez da (-a-siña x) = -a cos by cos cz x. (a cosar) Similarly - a² cos by cos cez & cos ax es rb cos by Coscz cos ar dari over = (-a-6-44) cos ax cosby cosce Eegin value Scanned with CamScanner