<p> rkf4(y0,x0,x1,n,f) </p>

48bd8e5c-13c9-436f-9962-2e8cc0d10d27 11 4 5 decimal

&[DATE] &[TIME] - &[FILENAME]

Hermite polynomials => n x H 1 - (k^n! (* (k! (n 2 k * - (! (* / 2 x * (n 2 k * -^* (k 0 n 2 / Floor sum :

y'' 2 x * (y' * - λ 1 - (y * + 0 ≡

Normalised wave function n x Ψ 1 π / (14 /^12 n^n! (* sqrt / * n x H * x 2^- 2 / exp * :

assign/collect plotting arguments x V 12 / x 2^* : x Ψ.0 0 x Ψ (2^12 / + : x Ψ.1 1 x Ψ (2^32 / + : x Ψ.2 2 x Ψ (2^52 / + : x Ψ.3 3 x Ψ (2^72 / + : 51 line_plot x V x Ψ.0 x Ψ.1 x Ψ.2 x Ψ.3 51 sys : 13 mat

4 x Ψ 2 ^

underscore #_# 13 mat

plot

<= inverse colors

Wave function for the 
harmonic oscillator n x Ψ n x H x 2^- 2 / exp * :

Equations in various font colors are horribly painful to use and turn a document to "cartoon style". Valery and myself have used few times just to show collabs how to use. The only ones I have conserved: red & blue to distinguish subscript from index. Further, if colors can't be shown on sheet background [grey 235 for instance] the document does not render pleasant. BTW: Smath [255,255,225] description is simply "delicious/comfortable". All those things aren't for color blind.

Probanility densities
of the eigenstates n x PDψ n x Ψ (2^:

The expectation function n x Es n x Ψ (2^x * :

The expectation value 4 x Es x 05 int 648

7 identity 100000001000000010000000100000001000000010000000177 mat

I 55 el 0 : 000000000000000000000000055 mat

The expectation value 4 x Es x 05 int 648

y0 x0 x1 n f rkf4 X 1 el x0 : Y 1 el y0 : Δ x1 x0 - n 1 - / : 13 mat i 2 n range k1 X i 1 - el Y i 1 - el f eval : k2 X i 1 - el Δ 2 / + Y i 1 - el k1 2 / Δ * + f eval : k3 X i 1 - el Δ 2 / + Y i 1 - el k2 2 / Δ * + f eval : k4 X i 1 - el Δ + Y i 1 - el k3 Δ * + f eval : Y i el Y i 1 - el k1 2 k2 * + 2 k3 * + k4 + 6 / Δ * + : X i el X i 1 - el Δ + : 61 line for X Y augment 31 line :

2 x * - y -

1 x y 3 nthroot * -

x y f 1 x y 3 nthroot * - :

y0 1 : x0 0 : x1 5 : n 200 : 14 mat

rkf y0 x0 x1 n f rkf4 :

Σ rkf 1 col rkf 2 col augment :

integral curve of

Σ 2 1.5 2 0.5 2 2 mat 2 1 sys

1 x x y 3 nthroot * -

rkf 01 0.0251 1.0248 0.0503 1.049 0.0754 1.0725 0.1005 1.0953 0.1256 1.1175 0.1508 1.139 0.1759 1.1599 0.201 1.18 0.2261 1.1994 0.2513 1.2182 112 mat

show 200 => matrix [1,1] ...type = rkf 11 mat