wave function (x,t). Consider a particle described by a time-independent, Gaussian wavefunction:(x) = Ne-ax²where a is a positive constant.a) Find the normalization constant N using )* (x)Þ(x)dxcomplex conjugate of . You can choose N to be real. In this case, ý is also real: * = b.1, where * is theb) Determine the mean value of the position x of the particle:a/* (x)x½(x)dx.c) Determine the mean value of x2:gi* (x )a²u(x)dx.

wave function (x,t). Consider a particle described by a time-independent, Gaussian wave function: V(x) = Ne-aa². where a is a positive constant. a) Find the normalization constant N using S v*(x)Þ(x)dx complex conjugate of y. You can choose N to be real. In this case, v is also real: * = v. 1, where * is the %3D b) Determine the mean value of the position x of the particle: * (x)x½(x)dx. c) Determine the mean value of x2: g? = | * (x)x²»(x)dx.

wave function (x,t). Consider a particle described by a time-independent, Gaussian wave function: V(x) = Ne-aa². where a is a positive constant. a) Find the normalization constant N using S v(x)Þ(x)dx complex conjugate of y. You can choose N to be real. In this case, v is also real: = v. 1, where * is the %3D b) Determine the mean value of the position x of the particle: * (x)x½(x)dx. c) Determine the mean value of x2: g? = | * (x)x²»(x)dx.