Recall that the Klein-Gordon equation for a particle moving in the presence of a potential V(a)= qb(z) in one dimension

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Recall That The Klein Gordon Equation For A Particle Moving In The Presence Of A Potential V A Qb Z In One Dimension 1 (21.67 KiB) Viewed 412 times

Recall that the Klein-Gordon equation for a particle moving in the presence of a potential V(a)= qb(z) in one dimension is given by 2 (ih-V(z)) ² 0(2,1)= (-(hc)² -(-(he)² + (me²)²) o(x, t). ² Consider a particle of energy E>0 incident on a potential barrier fo for x < 0, V(x) V for x > 0. 1. Writing (x, t)e(r), show that (E-V)²(x)=(-(hc)² -(-(hc)² + (m²)²) ox(x) 2. Show that the solution to this equation can be written as for r <0, E2 = (chk)² + (me²)², Og(x)= Aeike+Be-ikz Ceige for x>0, (E-V)² = (chq)² + (me²)².