00 V(x) 0 . Y(x,t)= Ae-ja)(Et-px) = V(x)=0, 0

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1 (2.69 KiB) Viewed 32 times

It is assumed that the particle is V(x)=0 except for the
boundaries x=0 and x=L, and V(x) is trapped in an infinitely large
potential well at the boundary.

2 (5.12 KiB) Viewed 32 times

The exact expression of the wave function, which is a solution
obtained by solving the one-dimension Schoedunger equation
independent of time inside the well after separating the given wave
function by variables, is as follows.

3 (2.53 KiB) Viewed 32 times

Suppose a particle lies in the ground state of the
potential energy well given above.
(a) In the ground state, we want to find the expectation
for standard deviation (uncertainty △x in the position of the
particle),△x of the measurement value for the position. Using
the given conditions and wave functions mentioned above, describe
the expected value of △x in the expression of L (calculation
process required)
(b)In the ground state, we want to find the expectations for the
standard deviation (uncertainty △px, in the momentum of the
particle), △px of the measurement for momentum. Using the
given conditions and wave functions mentioned above, describe the
expected value of △px in the expression of L (calculation process
required)
(c)Using the △x and △px values obtained above, induce
Heisenberg's Uncertainty Principle to be
△x△px>=ℏ/2.(calculation process required)
00 V(x) 0 .
Y(x,t)= Ae-ja)(Et-px) = V(x)=0, 0<x<L ; V(x)=0, x=0, L 9
V 2 sin L пл n X L