- #1
Boltzman Oscillation
- 233
- 26
- Homework Statement
- y'' = (r^2)y
- Relevant Equations
- characteristic equation
Hello I need to derive this equation from Grittfith's quantum book
$$ \frac{d^2y}{dr^2} = r^2y$$
I know I can use the characteristic equation:
$$m^2 = r^2 \rightarrow y = e^{r^2}$$
but the answer should be:
$$y=Ae^{\frac{-r^2}{2}} + Be^{\frac{r^2}{2}}$$
I know from Euler's formula that:
$$e^{ix} = cos(x)+isin(x)$$
but there is no imaginary number in y.
Can I absorb the imaginary constant into a constant B or A and then go from there?
$$ \frac{d^2y}{dr^2} = r^2y$$
I know I can use the characteristic equation:
$$m^2 = r^2 \rightarrow y = e^{r^2}$$
but the answer should be:
$$y=Ae^{\frac{-r^2}{2}} + Be^{\frac{r^2}{2}}$$
I know from Euler's formula that:
$$e^{ix} = cos(x)+isin(x)$$
but there is no imaginary number in y.
Can I absorb the imaginary constant into a constant B or A and then go from there?
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