Schrödinger Equation (in atomic unit)

$$ \left[-\frac{1}{2}\frac{d^2}{dx^2}+V(x)\right]\psi(x)=E\psi(x) $$ $$ x=[x_a, x_b],\hspace{1em}\psi(x_a)=\psi(x_b)=0 $$ $$ x_n=nh+x_a \hspace{1em}(n=0,1\cdots, N),\hspace{1em} h=(x_b-x_a)/N $$ Basis: $$ \psi(x)=\sum_i c_i \varphi_i(x),\hspace{2em} \varphi_i(x)= \left\{ \begin{aligned} & \frac{1}{\sqrt{h}} &&(x_i-h/2 \lt x \lt x_i+h/2) \\ & \frac{1}{2\sqrt{h}} &&(x = x_i\pm h/2) \\ & 0 &&(\text{otherwise}) \end{aligned} \right. $$

Input parameters

lower limit of x-axis x_a
upper limit of x-axis x_b
Number of divisions N

Potential V(x) (JavaScript), It can be described using theMath library:
let V = 0.5*x*x; return V;

Diagonalization method for real symmetric tridiagonal matrices	tqli math.eigs numeric.eig
Lower bound for eigenvalue output
Number of eigenvalues to output

Graph Settings

Auto	Graph Width (px)
Auto	Graph Height (px)
Auto	Aspect Ratio (x/y)
Auto	Aspect Ratio (x/y)	[ ,  ]
Auto	y-axis [Lower, Upper]	[ ,  ]

Eigenfunction Output Format

Select: Real Part Absolute Value Absolute Value Squared Real Part and Absolute Value Squared