Consider a quantum harmonic oscillator with potential energy V(x) = \(\frac{1}{2}mw^2x^2\), where m is the mass of the particle and ω  is the angular frequency. The wavefunctions ψn(x)  and energy levels En ​ are given by:

\(En=(n+\frac{1}{2})ℏω\),  n=0,1,2,…

The probability density ∣ψn(x)∣2  describes the likelihood of finding the particle at position x  for each state n. For which quantum state n is the probability of finding the particle at x=0 the highest?