As a 1-dimensional problem, you have Schrodinger's equation, given by: a -h? a2 iħ (x, t) =- at 2m Əx? 4(x, t) + V(x) Þ(x,t) Suppose for a specific V(x) and certain boundary conditions, the function w,(x, t) is a solution to the above equation and w2 (x, t) is also a solution. Show that 4(x, t) = a,(x, t) + b2(x, t) also solves the above equation, where a, b are complex numbers.
As a 1-dimensional problem, you have Schrodinger's equation, given by: a -h? a2 iħ (x, t) =- at 2m Əx? 4(x, t) + V(x) Þ(x,t) Suppose for a specific V(x) and certain boundary conditions, the function w,(x, t) is a solution to the above equation and w2 (x, t) is also a solution. Show that 4(x, t) = a,(x, t) + b2(x, t) also solves the above equation, where a, b are complex numbers.
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Transcribed Image Text:As a 1-dimensional problem, you have Schrodinger's equation, given by:
-h? a2
a
ih
h 4(x, t) =
at
2m Əx² ¥(x,t) + V(x) Þ(x,t)
Suppose for a specific V(x) and certain boundary conditions, the function w, (x, t) is a solution to the above
equation and 42 (x, t) is also a solution. Show that (x, t)
equation, where a, b are complex numbers.
a 41 (x, t) + b w2(x, t) also solves the above
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