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r=e("glslify"),i=e("h"),o=e("./control-panel-2"),a=e("./control-panel-2/gui");e("insert-css")("\ncanvas {\n  cursor: move;\n}\n"),e("regl")({pixelRatio:Math.min(window.devicePixelRatio,1.5),extensions:["oes_texture_float","oes_texture_float_linear"],attributes:{antialias:!1},onDone:e("fail-nicely")(function(t){var n=0,f=.5,u=n/f;window.innerWidth,window.innerHeight;function s(){v=!0}var c=window.state=o({hbar:o.Slider(.005,{min:1e-4,max:.1,step:1e-4}).onChange(s),aperture:o.Slider(.2,{min:.001,max:1,step:.001}).onChange(s)});a(c,i("p",null,["This page plots Eq. 3.40 from Feynman and Hibbs' ",i("a",{href:"http://store.doverpublications.com/0486477223.html",target:"blank"},"Quantum Mechanic and Path Integrals"),". It depicts the magnitude of the wavefunction for a particle passing through a known aperture at a known time. The function is computed by adding up all paths passing through the slit and taking into account interference of the particle with itself. Two slits aren't required for a particle to interfere with itself! As ℏ approaches zero, it approaches a sharp shadow."])),e("mouse-change")(function(e,t,r){0!==e&&(u=2*t/window.innerWidth,n=h+(d-h)*t/window.innerWidth,f=l+(p-l)*(1-r/window.innerHeight),u=n/f,v=!0)}),t._gl.canvas.addEventListener("touchmove",function(e){if(1===e.touches.length){e.preventDefault();var t=e.touches[0],r=t.clientX,i=t.clientY;u=2*r/window.innerWidth,n=h+(d-h)*r/window.innerWidth,f=l+(p-l)*(1-i/window.innerHeight),u=n/f,v=!0}}),window.addEventListener("wheel",function(e){e.preventDefault(),c.aperture=Math.min(1,Math.max(.001,c.aperture*Math.exp(.01*-e.deltaY)))}),document.body.appendChild(i("div",{class:"x-axis axis-label"},"Space ⟶")),document.body.appendChild(i("div",{class:"y-axis axis-label"},"Time ⟶"));var l=0,p=2,h=-2,d=2,m=t.texture([e("./plasma")]),x=t({uniforms:{uColormap:m,uAxes:[h,d,l,p],uT:function(){return f},uV:function(){return u},uX0:function(){return n},uB:function(){return c.aperture},uHbar:function(){return 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3.99982968972496e-12 + (x_0 * (9.154392157746574e-10 + (x_0 * (1.2500186247959882e-7 + (x_0 * (0.000012226278902417902 + (x_0 * (0.0008680295429417843 + (x_0 * (0.04121420907221998 + x_0))))))))));\n  }\n  return s1 / s2;\n}\n\nfloat polyG (float x_0) {\n  float s1, s2;\n  if (x_0 == 0.0) return 1.0;\n  float ax = x_0 < 0.0 ? -x_0 : x_0;\n  if (ax <= 1.0) {\n    s1 = 1.8695871016278324e-22 + (x_0 * (8.363544356306774e-19 + (x_0 * (1.375554606332618e-15 + (x_0 * (1.0826804113902088e-12 + (x_0 * (4.4534441586175015e-10 + (x_0 * (9.828524436884223e-8 + (x_0 * (0.000011513882611188428 + (x_0 * (0.0006840793809153931 + (x_0 * (0.018764858409257526 + (x_0 * (0.1971028335255234 + (x_0 * (0.5044420736433832))))))))))))))))))));\n    s2 = 1.8695871016278324e-22 + (x_0 * (8.391588162831187e-19 + (x_0 * (1.3879653125957886e-15 + (x_0 * (1.1027321506624028e-12 + (x_0 * (4.6068072814652043e-10 + (x_0 * (1.0431458965757199e-7 + (x_0 * (0.000012754507566772912 + (x_0 * (0.0008146791071843061 + (x_0 * (0.02536037414203388 + (x_0 * (0.33774898912002 + (x_0 * (1.4749575992512833 + x_0))))))))))))))))))));\n  } else {\n    x_0 = 1.0 / x_0;\n    s1 = 0.0 + (x_0 * (0.5044420736433832 + (x_0 * (0.1971028335255234 + (x_0 * (0.018764858409257526 + (x_0 * (0.0006840793809153931 + (x_0 * (0.000011513882611188428 + (x_0 * (9.828524436884223e-8 + (x_0 * (4.4534441586175015e-10 + (x_0 * (1.0826804113902088e-12 + (x_0 * (1.375554606332618e-15 + (x_0 * (8.363544356306774e-19 + (x_0 * 1.8695871016278324e-22)))))))))))))))))))));\n    s2 = 1.0 + (x_0 * (1.4749575992512833 + (x_0 * (0.33774898912002 + (x_0 * (0.02536037414203388 + (x_0 * (0.0008146791071843061 + (x_0 * (0.000012754507566772912 + (x_0 * (1.0431458965757199e-7 + (x_0 * (4.6068072814652043e-10 + (x_0 * (1.1027321506624028e-12 + (x_0 * (1.3879653125957886e-15 + (x_0 * (8.391588162831187e-19 + (x_0 * 1.8695871016278324e-22)))))))))))))))))))));\n  }\n  return s1 / s2;\n}\n\nfloat polyS (float x_0) {\n  float s1, s2;\n  if (x_0 == 0.0) return 0.5235987755982989;\n  float ax = x_0 < 0.0 ? -x_0 : x_0;\n  if (ax <= 1.0) {\n    s1 = 318016297876.5678 + (x_0 * (-44297951805.96978 + (x_0 * (2548908805.7337637 + (x_0 * (-62974148.62058625 + (x_0 * (708840.0452577386 + (x_0 * (-2991.8191940101983 + x_0))))))))));\n    s2 = 607366389490.0846 + (x_0 * (22441179564.534092 + (x_0 * (419320245.8981112 + (x_0 * (5173438.887700964 + (x_0 * (45584.78108065326 + (x_0 * (281.3762688899943 + x_0))))))))));\n  } else {\n    x_0 = 1.0 / x_0;\n    s1 = 0.0 + (x_0 * (-2991.8191940101983 + (x_0 * (708840.0452577386 + (x_0 * (-62974148.62058625 + (x_0 * (2548908805.7337637 + (x_0 * (-44297951805.96978 + (x_0 * 318016297876.5678)))))))))));\n    s2 = 1.0 + (x_0 * (281.3762688899943 + (x_0 * (45584.78108065326 + (x_0 * (5173438.887700964 + (x_0 * (419320245.8981112 + (x_0 * (22441179564.534092 + (x_0 * 607366389490.0846)))))))))));\n  }\n  return s1 / s2;\n}\n\nvec2 fresnel(float x) {\n  float x2, a, f, g, t, u;\n  vec2 result = vec2(0.5);\n\n  float xa = abs( x );\n  x2 = xa * xa;\n  if (x2 < 2.5625) {\n    t = x2 * x2;\n    result = xa * vec2(x2 * polyS(t), polyC(t));\n  } else if (xa <= 36974.0) {\n    x2 = xa * xa;\n    t = PI * x2;\n    u = 1.0 / (t * t);\n    t = 1.0 / t;\n    f = 1.0 - u * polyF(u);\n    g = t * polyG(u);\n    t = HALF_PI * x2;\n    float st = sin(t);\n    float ct = cos(t);\n    t = PI * xa;\n    result = 0.5 - (ct * vec2(f, g) + st * vec2(g, -f)) / t;\n  }\n  return x < 0.0 ? -result : result;\n}\n\n      uniform sampler2D uColormap;//, uSrc;\n      uniform float uT, uV, uB, uHbar, uM, uX0, uColorScaleFactor;\n      varying vec2 vXt;\n\n      #define PI 3.1415926535\n\n      vec4 colormap (float x) {\n        x = sqrt(x);\n        return texture2D(uColormap, vec2(x + 1.0 / 256.0 * (random(gl_FragCoord.xy) - 0.5), 0.5), 1.0);\n        //return texture2D(uColormap, vec2(x, 0.5), 1.0);\n      }\n\n      float u (vec2 xt, float sgn) {\n        float k = 1.0 + xt.y / uT;\n        return ((xt.x - uV * xt.y) + sgn * uB * k) / sqrt(PI * uHbar * xt.y / uM * k);\n      }\n\n      float psi(vec2 xt) {\n        vec2 SC = fresnel(u(xt, 1.0)) - fresnel(u(xt, -1.0));\n        return uM / (2.0 * PI * (uT + xt.y)) * 0.5 * dot(SC, SC);\n      }\n\n      void main () {\n        gl_FragColor = colormap(psi(vXt - vec2(uX0, uT)) * uColorScaleFactor);\n      }\n    ",""]),attributes:{xy:[-4,-4,0,4,4,-4]},scissor:{enable:!0,box:{x:0,y:function(e){return Math.max(0,Math.floor((f-l)/(p-l)*e.framebufferHeight))},width:function(e){return e.framebufferWidth},height:function(e){return e.framebufferHeight}}},depth:{enable:!1},count:3}),g=t({vert:"\n      precision highp float;\n      attribute vec2 xy;\n      uniform vec4 uAxes;\n      varying vec2 vXt;\n      void main () {\n        vec2 uv = xy * 0.5 + 0.5;\n        vXt = uAxes.xz + (uAxes.yw - uAxes.xz) * uv;\n        gl_Position = vec4(xy, 0, 1);\n      }\n    ",frag:r(["\n      precision highp float;\n#define GLSLIFY 1\n\n\n      highp float 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1.2544323709001127e-20 + (\n      x_0 * (4.5200143407412973e-17 + (\n        x_0 * (5.887545336215784e-14 + (\n          x_0 * (3.6014002958937136e-11 + (\n            x_0 * (1.1269922476399903e-8 + (\n              x_0 * (0.0000018462756734893055 + (\n                x_0 * (0.00015593440916415301 + (\n                  x_0 * (0.0064405152650885865 + (\n                    x_0 * (0.11688892585919138 + (\n                      x_0 * (0.7515863983533789 + (\n                        x_0 * (1.0)\n                      )))))))))))))))))));\n  } else {\n    x_0 = 1.0 / x_0;\n    s1 = 0.0 + (\n      x_0 * (0.4215435550436775 + (\n        x_0 * (0.1434079197807589 + (\n          x_0 * (0.011522095507358577 + (\n            x_0 * (0.000345017939782574 + (\n              x_0 * (0.0000046361374928786735 + (\n                x_0 * (3.055689837902576e-8 + (\n                  x_0 * (1.0230451416490724e-10 + (\n                    x_0 * (1.7201074326816183e-13 + (\n                      x_0 * (1.3428327623306275e-16 + (\n                        x_0 * 3.763297112699879e-20\n                      )))))))))))))))))));\n    s2 = 1.0 + (\n      x_0 * (0.7515863983533789 + (\n        x_0 * (0.11688892585919138 + (\n          x_0 * (0.0064405152650885865 + (\n            x_0 * (0.00015593440916415301 + (\n              x_0 * (0.0000018462756734893055 + (\n                x_0 * (1.1269922476399903e-8 + (\n                  x_0 * (3.6014002958937136e-11 + (\n                    x_0 * (5.887545336215784e-14 + (\n                      x_0 * (4.5200143407412973e-17 + (\n                        x_0 * 1.2544323709001127e-20\n                      )))))))))))))))))));\n  }\n  return s1 / s2;\n}\n\nfloat polyC (float x_0) {\n  float s1, s2;\n  if (x_0 == 0.0) return 1.0;\n  float ax = x_0 < 0.0 ? -x_0 : x_0;\n  if (ax <= 1.0) {\n    s1 = 1.0 + (x_0 * (-0.20552590095501388 + (x_0 * (0.018884331939670384 + (x_0 * (-0.0006451914356839651 + (x_0 * (0.000009504280628298596 + (x_0 * (-4.9884311457357354e-8))))))))));\n    s2 = 1.0 + (x_0 * (0.04121420907221998 + (x_0 * (0.0008680295429417843 + (x_0 * (0.000012226278902417902 + (x_0 * (1.2500186247959882e-7 + (x_0 * (9.154392157746574e-10 + (x_0 * 3.99982968972496e-12)))))))))));\n  } else {\n    x_0 = 1.0 / x_0;\n    s1 = 0.0 + (x_0 * (-4.9884311457357354e-8 + (x_0 * (0.000009504280628298596 + (x_0 * (-0.0006451914356839651 + (x_0 * (0.018884331939670384 + (x_0 * (-0.20552590095501388 + x_0))))))))));\n    s2 = 3.99982968972496e-12 + (x_0 * (9.154392157746574e-10 + (x_0 * (1.2500186247959882e-7 + (x_0 * (0.000012226278902417902 + (x_0 * (0.0008680295429417843 + (x_0 * (0.04121420907221998 + x_0))))))))));\n  }\n  return s1 / s2;\n}\n\nfloat polyG (float x_0) {\n  float s1, s2;\n  if (x_0 == 0.0) return 1.0;\n  float ax = x_0 < 0.0 ? -x_0 : x_0;\n  if (ax <= 1.0) {\n    s1 = 1.8695871016278324e-22 + (x_0 * (8.363544356306774e-19 + (x_0 * (1.375554606332618e-15 + (x_0 * (1.0826804113902088e-12 + (x_0 * (4.4534441586175015e-10 + (x_0 * (9.828524436884223e-8 + (x_0 * (0.000011513882611188428 + (x_0 * (0.0006840793809153931 + (x_0 * (0.018764858409257526 + (x_0 * (0.1971028335255234 + (x_0 * (0.5044420736433832))))))))))))))))))));\n    s2 = 1.8695871016278324e-22 + (x_0 * (8.391588162831187e-19 + (x_0 * (1.3879653125957886e-15 + (x_0 * (1.1027321506624028e-12 + (x_0 * (4.6068072814652043e-10 + (x_0 * (1.0431458965757199e-7 + (x_0 * (0.000012754507566772912 + (x_0 * (0.0008146791071843061 + (x_0 * (0.02536037414203388 + (x_0 * (0.33774898912002 + (x_0 * (1.4749575992512833 + x_0))))))))))))))))))));\n  } else {\n    x_0 = 1.0 / x_0;\n    s1 = 0.0 + (x_0 * (0.5044420736433832 + (x_0 * (0.1971028335255234 + (x_0 * (0.018764858409257526 + (x_0 * (0.0006840793809153931 + (x_0 * (0.000011513882611188428 + (x_0 * (9.828524436884223e-8 + (x_0 * (4.4534441586175015e-10 + (x_0 * (1.0826804113902088e-12 + (x_0 * (1.375554606332618e-15 + (x_0 * (8.363544356306774e-19 + (x_0 * 1.8695871016278324e-22)))))))))))))))))))));\n    s2 = 1.0 + (x_0 * (1.4749575992512833 + (x_0 * (0.33774898912002 + (x_0 * (0.02536037414203388 + (x_0 * (0.0008146791071843061 + (x_0 * (0.000012754507566772912 + (x_0 * (1.0431458965757199e-7 + (x_0 * (4.6068072814652043e-10 + (x_0 * (1.1027321506624028e-12 + (x_0 * (1.3879653125957886e-15 + (x_0 * (8.391588162831187e-19 + (x_0 * 1.8695871016278324e-22)))))))))))))))))))));\n  }\n  return s1 / s2;\n}\n\nfloat polyS (float x_0) {\n  float s1, s2;\n  if (x_0 == 0.0) return 0.5235987755982989;\n  float ax = x_0 < 0.0 ? -x_0 : x_0;\n  if (ax <= 1.0) {\n    s1 = 318016297876.5678 + (x_0 * (-44297951805.96978 + (x_0 * (2548908805.7337637 + (x_0 * (-62974148.62058625 + (x_0 * (708840.0452577386 + (x_0 * (-2991.8191940101983 + x_0))))))))));\n    s2 = 607366389490.0846 + (x_0 * (22441179564.534092 + (x_0 * (419320245.8981112 + (x_0 * (5173438.887700964 + (x_0 * (45584.78108065326 + (x_0 * (281.3762688899943 + x_0))))))))));\n  } else {\n    x_0 = 1.0 / x_0;\n    s1 = 0.0 + (x_0 * (-2991.8191940101983 + (x_0 * (708840.0452577386 + (x_0 * (-62974148.62058625 + (x_0 * (2548908805.7337637 + (x_0 * (-44297951805.96978 + (x_0 * 318016297876.5678)))))))))));\n    s2 = 1.0 + (x_0 * (281.3762688899943 + (x_0 * (45584.78108065326 + (x_0 * (5173438.887700964 + (x_0 * (419320245.8981112 + (x_0 * (22441179564.534092 + (x_0 * 607366389490.0846)))))))))));\n  }\n  return s1 / s2;\n}\n\nvec2 fresnel(float x) {\n  float x2, a, f, g, t, u;\n  vec2 result = vec2(0.5);\n\n  float xa = abs( x );\n  x2 = xa * xa;\n  if (x2 < 2.5625) {\n    t = x2 * x2;\n    result = xa * vec2(x2 * polyS(t), polyC(t));\n  } else if (xa <= 36974.0) {\n    x2 = xa * xa;\n    t = PI * x2;\n    u = 1.0 / (t * t);\n    t = 1.0 / t;\n    f = 1.0 - u * polyF(u);\n    g = t * polyG(u);\n    t = HALF_PI * x2;\n    float st = sin(t);\n    float ct = cos(t);\n    t = PI * xa;\n    result = 0.5 - (ct * vec2(f, g) + st * vec2(g, -f)) / t;\n  }\n  return x < 0.0 ? -result : result;\n}\n\n      uniform sampler2D uColormap;//, uSrc;\n      uniform float uT, uV, uB, uHbar, uM, uX0, uColorScaleFactor;\n      uniform vec4 uAxes;\n      uniform vec2 uRes;\n      varying vec2 vXt;\n\n      #define PI 3.1415926535\n\n      vec4 colormap (float x) {\n        x = sqrt(x);\n        return texture2D(uColormap, vec2(x + 1.0 / 256.0 * (random(gl_FragCoord.xy) - 0.5), 0.5), 1.0);\n        //return texture2D(uColormap, vec2(x, 0.5), 1.0);\n      }\n\n      float u (vec2 xt, float sgn) {\n        float k = 1.0 + xt.y / uT;\n        return ((xt.x - uV * xt.y) + sgn * uB * k) / sqrt(PI * uHbar * (xt.y + uT) / uM * k);\n      }\n\n      float step (float x) {\n        return x > 0.0 ? 1.0 : 0.0;\n      }\n\n      float psi(vec2 xt) {\n        return uM / (2.0 * PI * (uT + xt.y)) * (step(u(xt, 1.0)) - step(u(xt, -1.0)));\n      }\n\n      void main () {\n        gl_FragColor = colormap(psi(vXt - vec2(uX0, uT)) * uColorScaleFactor);\n        if (vXt.y - uT > (-uRes.y * 5.0 * (uAxes.w - uAxes.z)) && ((vXt.x - uV * uT) < -uB || (vXt.x - uV * uT) > uB)) gl_FragColor = vec4(1);\n      }\n    ",""]),attributes:{xy:[-4,-4,0,4,4,-4]},scissor:{enable:!0,box:{x:0,y:0,width:function(e){return e.framebufferWidth},height:function(e){return Math.max(0,Math.ceil((f-l)/(p-l)*e.framebufferHeight))}}},depth:{enable:!1},count:3}),v=!0;t.frame(function(){v&&(x(function(){b(),g()}),v=!1)})})}),e("insert-css")("\n.axis-label {\n  font-family: sans-serif;\n  color: white;\n  position: fixed;\n  font-weight: 200;\n  font-style: italic;\n}\n.x-axis {\n  bottom: 8px;\n  right: 10px;\n}\n.y-axis {\n  transform: translate(0, 100%) rotate(-90deg) translate(-50%, 0);\n  transform-origin: 0% 0%;\n  left: 8px;\n  bottom: 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