Consider that complex-valued functions $p(x)$ and $q(x)$ satisfy the simultaneous ordinary differential equations below: $$\frac{\mathrm{d}p(x)}{\mathrm{d}x} = -ib\, q(x)\exp(-2iax),$$ $$\frac{\mathrm{d}q(x)}{\mathrm{d}x} = -ib\, p(x)\exp(2iax).$$ Here, $i$ is the imaginary unit, and $a$ and $b$ are real constants. Let $f(x) = p(x)\exp(iax)$ and $g(x) = q(x)\exp(-iax)$. Let $a = 0.8$ and $b = 0.6$. Solve the simultaneous ordinary differential equations derived in Question II.1 using the initial values $f(0) = 1$ and $g(0) = 0$, and obtain $f(x)$ and $g(x)$.
Consider that complex-valued functions $p(x)$ and $q(x)$ satisfy the simultaneous ordinary differential equations below:
$$\frac{\mathrm{d}p(x)}{\mathrm{d}x} = -ib\, q(x)\exp(-2iax),$$
$$\frac{\mathrm{d}q(x)}{\mathrm{d}x} = -ib\, p(x)\exp(2iax).$$
Here, $i$ is the imaginary unit, and $a$ and $b$ are real constants. Let $f(x) = p(x)\exp(iax)$ and $g(x) = q(x)\exp(-iax)$.
Let $a = 0.8$ and $b = 0.6$. Solve the simultaneous ordinary differential equations derived in Question II.1 using the initial values $f(0) = 1$ and $g(0) = 0$, and obtain $f(x)$ and $g(x)$.