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ly(x, t = 0)|² = e exp (-). Show that at arbitrary time the probability %D %D density of the packet is lý(x,t)|² : x2 1 where L(t)Vn exp L²(t).

ly(x, t = 0)|² = e exp (-). Show that at arbitrary time the probability %D %D density of the packet is lý(x,t)|² : x2 1 where L(t)Vn exp L²(t).

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TOPIC: QUANTUM MECHANICS "WAVY PROPERTIES OF THE PARTICLE" 

Solve the following problem step by step, indicate your procedure and justify each step you give as well as your answer.

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Note  ħ=h/2π

Consider a Gaussian wave packet that at time t = 0 is given by ´ipox p(x,t = 0) = exp (* -) with 1 probability density 1 Tp(x,t = 0)|2 (-). Show that at arbitrary time the probability exp L2 x2 (-) where 1 density of the packet is p(x, t)|² : L(t)Vn exp L² (t) L(t) = L² + ħt? which shows how the packet widens as the particle m²L? moves
Transcribed Image Text:Consider a Gaussian wave packet that at time t = 0 is given by ´ipox p(x,t = 0) = exp (* -) with 1 probability density 1 Tp(x,t = 0)|2 (-). Show that at arbitrary time the probability exp L2 x2 (-) where 1 density of the packet is p(x, t)|² : L(t)Vn exp L² (t) L(t) = L² + ħt? which shows how the packet widens as the particle m²L? moves
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