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Version 2- More Waves, More Particles, More Duality
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| <!DOCTYPE html> | ||
| <html lang="EN"> | ||
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| <head> | ||
| <meta charset="utf-8"> | ||
| <meta name="viewport" content="width=device-width, initial-scale=1.0"> | ||
| <link rel="stylesheet" type="text/css" href="https://www.w3schools.com/w3css/4/w3.css"> | ||
| <link rel="stylesheet" type="text/css" href="styles.css"> | ||
| <title>Interactive Particle In A Box</title> | ||
| <script src="mathplus.js"></script> | ||
| <script src="https://cdn.jsdelivr.net/npm/p5@1.0.0/lib/p5.js"></script> | ||
| </head> | ||
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| <body> | ||
| <div id="containment"> | ||
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| <img id="burger" class="w3-btn w3-purple w3-card-4 w3-hover-deep-purple" src="./textures/burger.svg" width="5%" onClick="baropen()"/> | ||
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| <div id="sidebar" class="w3-sidebar w3-animate-opacity w3-khaki"> | ||
| <div id="navibar" class="w3-bar w3-khaki w3-card-4"> | ||
| <a href="index.html" class="w3-btn w3-bar-item w3-wide w3-large w3-ripple w3-purple w3-hover-deep-purple w3-bar-item">Home</a> | ||
| <span class="w3-bar-item"><b>Particle In A Box</b> | ||
| <input type="button" class="helpButton w3-card-2 w3-ripple w3-round w3-purple w3-hover-deep-purple" value="?" onClick="helpopen('Introduction')"/> | ||
| </span> | ||
| </div> | ||
| <div class="w3-container w3-red"><b>Position</b> Arrowheads correspond to units of distance.</div> | ||
| <div class="w3-container w3-blue"><b>Real</b> Axis of Wavefunction<input type="button" class="helpButton w3-card-2 w3-ripple w3-round w3-aqua w3-hover-blue" value="?" onClick="helpopen('Wavefunctions')"/></div> | ||
| <div class="w3-container w3-green"><b>Imaginary</b> Axis of Wavefunction<input type="button" class="helpButton w3-card-2 w3-ripple w3-round w3-aqua w3-hover-blue" value="?" onClick="helpopen('Complex')"/></div> | ||
| <div class="w3-container w3-orange"><input id="showMOM" type="checkbox" autocomplete="off"/><b>Momentum</b> Display Momentum Wavefunction<input type="button" class="helpButton w3-card-2 w3-ripple w3-round w3-aqua w3-hover-blue" value="?" onClick="helpopen('momentum')"/></div> | ||
| <div class="w3-container">Play Speed(1=RealTime):</br> | ||
| <input id="timeAcc" type="number" step="0.2" value="1" autocomplete="off" style="width:4em"/> | ||
| <input id="timeRes" type="button" class="w3-btn w3-card-4 w3-ripple w3-round w3-purple w3-hover-deep-purple" value="time=0" onClick="resetTime()"/> | ||
| </div> | ||
| <div class="w3-container"> | ||
| <span class="label">X Scaling:</span> | ||
| <input id="scaleSlider" class="usrinput" type="range" min="0.2" max="2" value="1" step="0.1" autocomplete="off"/> | ||
| </div> | ||
| <div class="w3-container"> | ||
| <span class="label">Y Scaling:</span> | ||
| <input id="yScaleSlider" class="usrinput" type="range" min="0.2" max="2" value="1" step="0.1" autocomplete="off"/> | ||
| </div> | ||
| <div class="w3-container"> | ||
| <span id="massLabel" class="label">Mass: 25</span> | ||
| <input id="massSlider" class="usrinput" type="range" min="0.1" max="100" value="25" step="0.1" autocomplete="off"/> | ||
| </div> | ||
| <div class="w3-container"> | ||
| <span id="LLabel" class="label">Length "L": 4</span> | ||
| <input id="LSlider" class="usrinput" type="range" min="0.1" max="10" value="4" step="0.1" autocomplete="off"/> | ||
| </div> | ||
| <div class="w3-container"> | ||
| <div class="w3-red w3-container w3-card-4"> | ||
| <div class="w3-container"> | ||
| <span class="label">*No. of points:</span> | ||
| <input id="detailIn" type="number" class="usrinput" style="width: 5em;" min="1" step="10" value="256" autocomplete="off"/> | ||
| </div> | ||
| <div id="psiequation" class="w3-bar w3-panel w3-small w3-deep-orange w3-card-4 w3-round-large"> | ||
| <img class="w3-bar-item" src="./equations/psi.gif" alt="psi equals the sum of coefficents multiplied by their corresponding n-ket"/> | ||
| <input type="button" class="helpButton w3-card-2 w3-ripple w3-round w3-aqua w3-hover-blue" value="? n" onClick="helpopen('QuantumNumbers')"/> | ||
| <input type="button" class="helpButton w3-card-2 w3-ripple w3-round w3-aqua w3-hover-blue" value="? C" onClick="helpopen('Coefficients')"/> | ||
| </div> | ||
| <div class="w3-container"> | ||
| <span class="label">Represent as Reflection:</span> | ||
| <input id="standingBox" type="checkbox" autocomplete="off"/> | ||
| <input type="button" class="helpButton w3-card-2 w3-ripple w3-round w3-purple w3-hover-deep-purple" value="?" onClick="helpopen('Reflection')"/> | ||
| </div> | ||
| <div class="w3-green w3-panel w3-card-4"> | ||
| <div><input type="radio" name="coeffMode" value="manual" checked autocomplete="off"/> | ||
| *Manually Input Coefficients:<input type="button" class="helpButton w3-card-2 w3-ripple w3-round w3-aqua w3-hover-blue" value="?" onClick="helpopen('Manual')"/></div> | ||
| <input id="cInput" value="1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1" autocomplete="off"/> | ||
| </div> | ||
| <div class="w3-teal w3-panel w3-card-4"> | ||
| <div><input type="radio" name="coeffMode" value="function" autocomplete="off"/> | ||
| Define <b>C</b>n=<b>f</b>(n,t,u,w)<input type="button" class="helpButton w3-card-2 w3-ripple w3-round w3-aqua w3-hover-blue" value="?" onClick="helpopen('FunkMode')"/></div> | ||
| <div id="maxNLabel"><b>*</b>Max value of n: 16</div> | ||
| <input id="maxNSlider" type="range" min="1" max="32" value="16" step="1" autocomplete="off"/> | ||
| <div id="Udiv"> | ||
| <div id="Ulabel"><b>u</b> = 1 + 0i</div> | ||
| <input id="sliderURe" type="range" min="-10" max="10" value="1" step="0.1" autocomplete="off"/> | ||
| <input id="sliderUIm" type="range" min="-10" max="10" value="0" step="0.1" autocomplete="off"/> | ||
| </div> | ||
| <div id="Wdiv"> | ||
| <div id="Wlabel"><b>w</b> = 1 + 0i</div> | ||
| <input id="sliderWRe" type="range" min="-10" max="10" value="1" step="0.1" autocomplete="off"/> | ||
| <input id="sliderWIm" type="range" min="-10" max="10" value="0" step="0.1" autocomplete="off"/> | ||
| </div> | ||
| <div><b>*f</b>(n,t,u,w)=<input id="fInput" value="exp(-((n-u)^2)/(2*w^2))" autocomplete="off"/></div> | ||
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| </div> | ||
| <div class="w3-panel"> | ||
| <input id="cButton" type="button" class="w3-btn w3-card-4 w3-ripple w3-round w3-khaki w3-hover-deep-orange" value="Apply" onClick="buttFunk()"/> | ||
| *Needs "Apply" | ||
| </div> | ||
| </div> | ||
| </div> | ||
| <div> | ||
| <select id="setters"> | ||
| <option value="maxReU">Real U Slider: Max</option> | ||
| <option value="minReU">Real U Slider: Min</option> | ||
| <option value="maxImU">Imaginary U Slider: Max</option> | ||
| <option value="minImU">Imaginary U Slider: Min</option> | ||
| <option value="maxReW">Real W Slider: Max</option> | ||
| <option value="minReW">Real W Slider: Min</option> | ||
| <option value="maxImW">Imaginary W Slider: Max</option> | ||
| <option value="minImW">Imaginary W Slider: Min</option> | ||
| <option value="massMax">Mass Slider: Max</option> | ||
| <option value="massMin">Mass Slider: Min</option> | ||
| <option value="maxNMax">Max N Slider: Max</option> | ||
| <option value="lengthMax">Length Slider: Max</option> | ||
| <option value="lengthMin">Length Slider: Min</option> | ||
| </select> | ||
| <div> | ||
| <input id="setVal" type="number" step="1" value="1" autocomplete="off"/> | ||
| <input id="setBut" type="button" class="w3-btn w3-card-4 w3-ripple w3-round w3-purple w3-hover-deep-purple" value="Set" onClick="advSetting()"/> | ||
| </div> | ||
| </div> | ||
| </div> | ||
| <img id="sideclose" class="w3-btn w3-card-4 w3-ripple w3-purple w3-hover-deep-purple w3-bar-item" src="./textures/doublearrow.svg" onClick="barclose()"/> | ||
| </div> | ||
| <div id="helpPanelIntroduction" style="display:none" class="help-panel w3-panel w3-card-4 w3-blue w3-display-middle w3-display-container"> | ||
| <h3>Help- "Particle In A Box"</h3> | ||
| <img id="eqNket" src="./equations/BOXnket.gif"/> | ||
| <p>This is a particle perfectly confined to a region of Length "L". Or, if you like, the quantum equivalent of a guitar string.</p> | ||
| <p>In reality this situation is very unphysical. In order to perfectly confine the particle to a region, you need an infinite wall of energy to stop it leaking out.</p> | ||
| <p>But assuming it to be possible, greatly simplifies a lot of the maths, in fact each energy state is just a sine or cosine wave of a specific frequency. This is because, like a guitar string, each of the end points are fixed in place at 0, meaning only certain frequencies are allowed. In a guitar string the waves bounce of the end points and interact with the waves coming in the other direction. A very similar phenomenon happens in this simulation and you can see the particle "interacting with itself" by checking the box marked "Represent As Reflection".</p> | ||
| <p>See Also: Standing Waves, Self-Interaction</p> | ||
| <input id="helpClose" type="button" class="w3-btn w3-card-4 w3-ripple w3-display-topright w3-purple w3-hover-deep-purple" value="X" onClick="helpclose('Introduction')"/> | ||
| </div> | ||
| <div id="helpPanelReflection" style="display:none" class="help-panel w3-panel w3-card-4 w3-blue w3-display-middle w3-display-container"> | ||
| <h3>Help- "Reflection"</h3> | ||
| <p>This will display show a decomposition of the wavefunction as two "free particles" moving in opposite directions. By adding these two together you get the original wavefunction.</p> | ||
| <p>At each wall the arrows pointing into it will be exactly opposite the arrows coming out of it. This may not seem like a reflection but when polarised light reflects off a surface it rotates by a full 180 degrees in the same way and so does the sound wave in a guitar string. This exact opposition also means they cancel out and keep the waveunction at zero at each of the end points.</p> | ||
| <p>See Also: Standing Waves, Sine and Cosine as Exponentials</p> | ||
| <input id="helpClose" type="button" class="w3-btn w3-card-4 w3-ripple w3-display-topright w3-purple w3-hover-deep-purple" value="X" onClick="helpclose('Reflection')"/> | ||
| </div> | ||
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| <script src="boxSketch.js"></script> | ||
| <script src="panels.js"></script> | ||
| </body> | ||
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| </html> |
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