A wave function is given by the equation $($x$,$t$)=$Aei$($kx$$t$)($x$,$t$)=$Aei$($kx$$t$).$

$$ Part $($a$)$

Calculate $22$m$2($x$,$t$)$x$222$m$2($x$,$t$)$x$2.$

$$

$$ Part $($b$)$

Calculate $$ i$($x$,$t$)$ti$($x$,$t$)$t$.$

$$

$$ Part $($c$)$

Based on your answers to parts $($a$)$ and $($b$),$ does the function $($x$,$t$)=$Aei$($kx$$t$)($x$,$t$)=$Aei$($kx$$t$)$ satisfy the time$-$dependent Schrodinger equation?