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 Problem Statement
 Problem statement attached as image
 Relevant Equations
 Schrodinger equation
##U_1 \otimes U_2 = (1 i H_1 \ dt) \otimes (1 i H_2 \ dt)##
We can write ##  \phi_i(t) > \ = U_i(t)  \phi_i(0)>## where i can be 1 or 2 depending on the subsystem. The ## U ##'s are unitary time evolution operators.
Writing as tensor product we get
## \phi_1 \phi_2> = (1 i H_1 \ dt)  \phi_1(0)> \otimes \ (1 i H_2 \ dt)  \phi_2(0)> ##
Since these states are normalised we may write
## 1 = < \phi_1 \phi_2  \phi_1 \phi_2 > = < \phi_1(0) 1 + H^2_1 dt^2  \phi_1(0)> < \phi_2(0) 1 + H^2_2 dt^2  \phi_2(0)> ##
This is as far as I've gotten. Any help would be appreciated.
We can write ##  \phi_i(t) > \ = U_i(t)  \phi_i(0)>## where i can be 1 or 2 depending on the subsystem. The ## U ##'s are unitary time evolution operators.
Writing as tensor product we get
## \phi_1 \phi_2> = (1 i H_1 \ dt)  \phi_1(0)> \otimes \ (1 i H_2 \ dt)  \phi_2(0)> ##
Since these states are normalised we may write
## 1 = < \phi_1 \phi_2  \phi_1 \phi_2 > = < \phi_1(0) 1 + H^2_1 dt^2  \phi_1(0)> < \phi_2(0) 1 + H^2_2 dt^2  \phi_2(0)> ##
This is as far as I've gotten. Any help would be appreciated.
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