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 $\omega$  is the angular frequency. The wavefunctions ψ_n(x) $\psi_n(x)$  and energy levels E_n $E_n$ ​ are given by:

\(En=(n+\frac{1}{2})ℏω\),  n=0,1,2,…

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