Hi, so i am looking at the quantization of the harmonic oscillator and i have the following equation...(adsbygoogle = window.adsbygoogle || []).push({});

ψ''+ (2ε-y[itex]^{2}[/itex])ψ=0

I am letting y[itex]\rightarrow[/itex] [itex]\infty[/itex] to get...

ψ''- y[itex]^{2}[/itex]ψ=0

It says the solution to this equation in the same limit is...

ψ= Ay[itex]^{m}[/itex]e[itex]^{\pm y^{2}/2}[/itex]

The positive possibility in the exponential is ignored since it is not in the physical Hilbert space. My question is how did they solve this differential equation? I have read a couple websites and it says that you just have to "guess" it... however, is there a logical way to why you would guess this? Thank you

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Quantum Harmonic Oscillator Differential Equation help

**Physics Forums | Science Articles, Homework Help, Discussion**