`); let searchUrl = `/search/`; history.forEach((elem) => { prevsearch.find('#prevsearch-options').append(`
${elem} `); }); } $('#search-pretype-options').empty(); $('#search-pretype-options').append(prevsearch); let prevbooks = $(false); [ {title:"Recently Opened Textbooks", books:previous_books}, {title:"Recommended Textbooks", books:recommended_books} ].forEach((book_segment) => { if (Array.isArray(book_segment.books) && book_segment.books.length>0 && nsegments<2) { nsegments+=1; prevbooks = $(`
${book_segment.title} `); let searchUrl = "/books/xxx/"; book_segment.books.forEach((elem) => { prevbooks.find('#prevbooks-options'+nsegments.toString()).append(`
${elem.title} ${ordinal(elem.edition)} ${elem.author} `); }); } $('#search-pretype-options').append(prevbooks); }); } function anon_pretype() { let prebooks = null; try { prebooks = JSON.parse(localStorage.getItem('PRETYPE_BOOKS_ANON')); }catch(e) {} if ('previous_books' in prebooks && 'recommended_books' in prebooks) { previous_books = prebooks.previous_books; recommended_books = prebooks.recommended_books; if (typeof PREVBOOKS !== 'undefined' && Array.isArray(PREVBOOKS)) { new_prevbooks = PREVBOOKS; previous_books.forEach(elem => { for (let i = 0; i < new_prevbooks.length; i++) { if (elem.id == new_prevbooks[i].id) { return; } } new_prevbooks.push(elem); }); new_prevbooks = new_prevbooks.slice(0,3); previous_books = new_prevbooks; } if (typeof RECBOOKS !== 'undefined' && Array.isArray(RECBOOKS)) { new_recbooks = RECBOOKS; for (let j = 0; j < new_recbooks.length; j++) { new_recbooks[j].viewed_at = new Date(); } let insert = true; for (let i=0; i < recommended_books.length; i++){ for (let j = 0; j < new_recbooks.length; j++) { if (recommended_books[i].id == new_recbooks[j].id) { insert = false; } } if (insert){ new_recbooks.push(recommended_books[i]); } } new_recbooks.sort((a,b)=>{ adate = new Date(2000, 0, 1); bdate = new Date(2000, 0, 1); if ('viewed_at' in a) {adate = new Date(a.viewed_at);} if ('viewed_at' in b) {bdate = new Date(b.viewed_at);} // 100000000: instead of just erasing the suggestions from previous week, // we just move them to the back of the queue acurweek = ((new Date()).getDate()-adate.getDate()>7)?0:100000000; bcurweek = ((new Date()).getDate()-bdate.getDate()>7)?0:100000000; aviews = 0; bviews = 0; if ('views' in a) {aviews = acurweek+a.views;} if ('views' in b) {bviews = bcurweek+b.views;} return bviews - aviews; }); new_recbooks = new_recbooks.slice(0,3); recommended_books = new_recbooks; } localStorage.setItem('PRETYPE_BOOKS_ANON', JSON.stringify({ previous_books: previous_books, recommended_books: recommended_books })); build_popup(); } } var whiletyping_search_object = null; var whiletyping_search = { books: [], curriculum: [], topics: [] } var single_whiletyping_ajax_promise = null; var whiletyping_database_initial_burst = 0; //number of consecutive calls, after 3 we start the 1 per 5 min calls function get_whiletyping_database() { //gets the database from the server. // 1. by validating against a local database value we confirm that the framework is working and // reduce the ammount of continuous calls produced by errors to 1 per 5 minutes. return localforage.getItem('whiletyping_last_attempt').then(function(value) { if ( value==null || (new Date()) - (new Date(value)) > 1000*60*5 || (whiletyping_database_initial_burst < 3) ) { localforage.setItem('whiletyping_last_attempt', (new Date()).getTime()); // 2. Make an ajax call to the server and get the search database. let databaseUrl = `/search/whiletype_database/`; let resp = single_whiletyping_ajax_promise; if (resp === null) { whiletyping_database_initial_burst = whiletyping_database_initial_burst + 1; single_whiletyping_ajax_promise = resp = new Promise((resolve, reject) => { $.ajax({ url: databaseUrl, type: 'POST', data:{csrfmiddlewaretoken: "tAjOkYZKhO2sQys3mei5k1MRBF8CIAhLY2OIe0R1ax30wMZyxYzuxDrsVDpSZ7cx"}, success: function (data) { // 3. verify that the elements of the database exist and are arrays if ( ('books' in data) && ('curriculum' in data) && ('topics' in data) && Array.isArray(data.books) && Array.isArray(data.curriculum) && Array.isArray(data.topics)) { localforage.setItem('whiletyping_last_success', (new Date()).getTime()); localforage.setItem('whiletyping_database', data); resolve(data); } }, error: function (error) { console.log(error); resolve(null); }, complete: function (data) { single_whiletyping_ajax_promise = null; } }) }); } return resp; } return Promise.resolve(null); }).catch(function(err) { console.log(err); return Promise.resolve(null); }); } function get_whiletyping_search_object() { // gets the fuse objects that will be in charge of the search if (whiletyping_search_object){ return Promise.resolve(whiletyping_search_object); } database_promise = localforage.getItem('whiletyping_database').then(function(database) { return localforage.getItem('whiletyping_last_success').then(function(last_success) { if (database==null || (new Date()) - (new Date(last_success)) > 1000*60*60*24*30 || (new Date('2023-04-25T00:00:00')) - (new Date(last_success)) > 0) { // New database update return get_whiletyping_database().then(function(new_database) { if (new_database) { database = new_database; } return database; }); } else { return Promise.resolve(database); } }); }); return database_promise.then(function(database) { if (database) { const options = { isCaseSensitive: false, includeScore: true, shouldSort: true, // includeMatches: false, // findAllMatches: false, // minMatchCharLength: 1, // location: 0, threshold: 0.2, // distance: 100, // useExtendedSearch: false, ignoreLocation: true, // ignoreFieldNorm: false, // fieldNormWeight: 1, keys: [ "title" ] }; let curriculum_index={}; let topics_index={}; database.curriculum.forEach(c => curriculum_index[c.id]=c); database.topics.forEach(t => topics_index[t.id]=t); for (j=0; j
Solutions
Textbooks
`); } function build_solutions() { if (Array.isArray(solution_search_result)) { const viewAllHTML = userSubscribed ? `View All` : ''; var solutions_section = $(` Solutions ${viewAllHTML} `); let questionUrl = "/questions/xxx/"; let askUrl = "/ask/question/xxx/"; solution_search_result.forEach((elem) => { let url = ('course' in elem)?askUrl:questionUrl; let solution_type = ('course' in elem)?'ask':'question'; let subtitle = ('course' in elem)?(elem.course??""):(elem.book ?? "")+" "+(elem.chapter?"Chapter "+elem.chapter:""); solutions_section.find('#whiletyping-solutions').append(` ${elem.text} ${subtitle} `); }); $('#search-solution-options').empty(); if (Array.isArray(solution_search_result) && solution_search_result.length>0){ $('#search-solution-options').append(solutions_section); } MathJax.typesetPromise([document.getElementById('search-solution-options')]); } } function build_textbooks() { $('#search-pretype-options').empty(); $('#search-pretype-options').append($('#search-solution-options').html()); if (Array.isArray(textbook_search_result)) { var books_section = $(` Textbooks View All `); let searchUrl = "/books/xxx/"; textbook_search_result.forEach((elem) => { books_section.find('#whiletyping-books').append(` ${elem.title} ${ordinal(elem.edition)} ${elem.author} `); }); } if (Array.isArray(textbook_search_result) && textbook_search_result.length>0){ $('#search-pretype-options').append(books_section); } } function build_popup(first_time = false) { if ($('#search-text').val()=='') { build_pretype(); } else { solution_and_textbook_search(); } } var search_text_out = true; var search_popup_out = true; const is_login = false; function pretype_setup() { $('#search-text').focusin(function() { $('#search-popup').addClass('show'); resize_popup(); search_text_out = false; }); $( window ).resize(function() { resize_popup(); }); $('#search-text').focusout(() => { search_text_out = true; if (search_text_out && search_popup_out) { $('#search-popup').removeClass('show'); } }); $('#search-popup').mouseenter(() => { search_popup_out = false; }); $('#search-popup').mouseleave(() => { search_popup_out = true; if (search_text_out && search_popup_out) { $('#search-popup').removeClass('show'); } }); $('#search-text').on("keyup", delay(() => { build_popup(); }, 200)); build_popup(true); let prevbookUrl = `/search/pretype_books/`; if (is_login) { $.ajax({ url: prevbookUrl, method: 'POST', data:{csrfmiddlewaretoken: "tAjOkYZKhO2sQys3mei5k1MRBF8CIAhLY2OIe0R1ax30wMZyxYzuxDrsVDpSZ7cx"}, success: function(response){ previous_books = response.previous_books; recommended_books = response.recommended_books; build_popup(); }, error: function(response){ console.log(response); } }); } else { let prebooks = null; try { prebooks = JSON.parse(localStorage.getItem('PRETYPE_BOOKS_ANON')); }catch(e) {} if (prebooks && 'previous_books' in prebooks && 'recommended_books' in prebooks) { anon_pretype(); } else { $.ajax({ url: prevbookUrl, method: 'POST', data:{csrfmiddlewaretoken: "tAjOkYZKhO2sQys3mei5k1MRBF8CIAhLY2OIe0R1ax30wMZyxYzuxDrsVDpSZ7cx"}, success: function(response){ previous_books = response.previous_books; recommended_books = response.recommended_books; build_popup(); }, error: function(response){ console.log(response); } }); } } } $( document ).ready(pretype_setup); $( document ).ready(function(){ $('#search-popup').on('click', '.search-view-item', function(e) { e.preventDefault(); let autoCompleteSearchViewUrl = `/search/autocomplete_search_view/`; let objectUrl = $(this).attr('href'); let selectedId = $(this).data('objid'); let searchResults = []; $("#whiletyping-solutions").find("a").each(function() { let is_selected = selectedId === $(this).data('objid'); searchResults.push({ objectId: $(this).data('objid'), contentType: $(this).data('contenttype'), category: $(this).data('category'), selected: is_selected }); }); $("#whiletyping-books").find("a").each(function() { let is_selected = selectedId === $(this).data('objid'); searchResults.push({ objectId: $(this).data('objid'), contentType: $(this).data('contenttype'), category: $(this).data('category'), selected: is_selected }); }); $.ajax({ url: autoCompleteSearchViewUrl, method: 'POST', data:{ csrfmiddlewaretoken: "tAjOkYZKhO2sQys3mei5k1MRBF8CIAhLY2OIe0R1ax30wMZyxYzuxDrsVDpSZ7cx", query: $('#search-text').val(), searchObjects: JSON.stringify(searchResults) }, dataType: 'json', complete: function(data){ window.location.href = objectUrl; } }); }); });
FAQs
As for the length of the box increases, the energy of a particle in one-dimensional box decreases. Since the difference in energy levels is governed directly by energy, the gap or space between energy levels decreases with a decrease in energy.
What is a particle confined to a one-dimensional box? ›
A particle in a 1-dimensional box is a fundamental quantum mechanical approximation describing the translational motion of a single particle confined inside an infinitely deep well from which it cannot escape.
What is the formula for the particle in a one-dimensional box? ›
Thus the normalized wave function of a particle in a box is. The energy of the particle in a 1-d box can be mathematically expressed as, E n = n 2 π 2 ℏ 2 2 m L 2 where n is a principal quantum number (n=1,2,3,4,......), L is the length of the box.
How do you solve a particle in a box problem? ›
The goal is to find the energy E (independent of x) and the wavefunction ψ(x), where 0<x<1. The usual method is to guess an energy E′, then start from x=0 and advance a small step dx until reach x=1. Check if ψ(1)=0.
When the length of the one-dimensional box is made larger the energy levels move? ›
In the particle/box problem, the possible wavelengths are set by the dimensions of the box; a bigger box allows longer wavelengths -> lower energies.
What is the boundary condition for a particle in a 1d box or an infinite square well? ›
The boundary conditions are that the wavefunction must go to 0 at the ends of the box, in accordance with the first postulate. So B=0 and the cosine term must vanish. Focusing only on what has not vanished from the solutions, the second boundary condition, ψ(a)=0, can be applied.
Is a particle 1-dimensional? ›
Actually, a particle is a zero-dimensional object. That is, it occupies no space, just a single point (if that much).
Is the energy of a particle in a one-dimensional box quantized? ›
The energy associated with a particle in a one-dimensional box is quantized because the particle is confined to a finite region of space. This means that the particle can only occupy certain discrete energy levels, and not any continuous range of energies.
Why a particle trapped in a box Cannot be at rest? ›
If the particle in a box has zero energy, it will be at rest inside the well and it violates Heisenberg's Uncertainty Principle. Thus, the minimum energy possessed by a particle is not equal to zero.
What is the Schrodinger equation for a particle in one dimension? ›
ψ(x,t)=Beik1xe−iEt/ℏ for x > 0, where k1 corresponds to the slower speed the particle will have after climbing the hill. Schrödinger's equation requires that the wave function have no discontinuities and no kinks (discontinuities in slope) so the x<0 and x>0 wave functions must match smoothly at the origin.
The dimensions of a box formula is pretty straightforward: length x width x height.
What is the particle in a box method? ›
The particle in a box model (also known as the infinite potential well or the infinite square well) describes a particle free to move in a small space surrounded by impenetrable barriers. The model is mainly used as a hypothetical example to illustrate the differences between classical and quantum systems.
What is the equation of a particle? ›
The equation of motion of a particle of mass 1 g is d2xdt2+π2x=0, where x is displacement (in m) from mean position.
What is the one-dimensional potential step? ›
In quantum mechanics and scattering theory, the one-dimensional step potential is an idealized system used to model incident, reflected and transmitted matter waves. The problem consists of solving the time-independent Schrödinger equation for a particle with a step-like potential in one dimension.
When an electron is trapped in a one-dimensional box of length 0.1 nm? ›
An electron is trapped in a one-dimensional box of length 0.1nm. For an electron in the given box, the mass can be taken as the electron mass = 9.109 x 10^-31 kg. Therefore, the energy required to excite the electron from its ground state to the fifth excited state is 3.69 x 10^-19 J.
What happens when particle size increases? ›
The increase in particle size results to lower surface area. The surface area is important for the interaction of molecules to one another. The lower the surface area, the lower the interactions such as collisions between the molecules.
What happens to the volume of a box when the measurements are doubled? ›
If you double one dimension, the volume doubles. If you double two dimensions, the volume quadruples. When all dimensions are doubled, the volume increases eight times.
What is the energy of the particle if L is the length of the one-dimensional box? ›
Particle in a one-dimensional box is a concept in Quantum mechanics that represents a particle in a space containing energy levels. The total energy of the particle for a one-dimensional box of length L is E n = n 2 h 2 8 m L 2 .
How much is the volume increased if the lengths of all sides of a box are doubled? ›
If all the lengths are doubled, the new volume = 2a*2b*2c = 8abc. So on doubling all the three sides of a box, the volume increases 8-fold or by 700%.
