Hi, could someone show me the steps to solve the equation(adsbygoogle = window.adsbygoogle || []).push({});

d^2y/dx^2 = -ky

for the solution

A*exp(i*sqrt(k)*x) + B*exp(-i*sqrt(k)*x)

?

I am trying to solve the time independent Schrodinger equation for a free particle, and the above question is of the same form. Wikipedia says it is the above solution, and I can kind of see where it's going in doing some of the math for myself, but am stuck at several places. Don't ask me what I did, it will not help me for you to correct me at steps, I just need to see it done so that I can "assimilate" the knowledge for me to use in other problems (I am rather inexperienced with these types of (O)DEs, and I'm learning subjects in tandem to learn them, quantum mechanics I would like to learn, and DEs I would like to strengthen my knowledge of; it's just how I learn best, don't ask me why).

Thanks,

linear

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# Steps for solving ODE

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