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  62.   <div class="section" id="module-sympy.physics.qho_1d">
    63. 

  63. <span id="quantum-harmonic-oscillator-in-1-d"></span><h1>Quantum Harmonic Oscillator in 1-D<a class="headerlink" href="#module-sympy.physics.qho_1d" title="Permalink to this headline"></a></h1>
    64. 

  64. <dl class="py function">
    65. 

  65. <dt id="sympy.physics.qho_1d.E_n">
    66. 

  66. <code class="sig-prename descclassname">sympy.physics.qho_1d.</code><code class="sig-name descname">E_n</code><span class="sig-paren">(</span><em class="sig-param"><span class="n">n</span></em>, <em class="sig-param"><span class="n">omega</span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/sympy/sympy/blob/46469d714a095fde59f9c4d83aaa528c68b0be0f/sympy/physics/qho_1d.py#L41-L64"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#sympy.physics.qho_1d.E_n" title="Permalink to this definition"></a></dt>
    67. 

  67. <dd><p>Returns the Energy of the One-dimensional harmonic oscillator</p>
    68. 

  68. <dl class="simple">
    69. 

  69. <dt><code class="docutils literal notranslate"><span class="pre">n</span></code></dt><dd><p>the “nodal” quantum number</p>
    70. 

  70. </dd>
    71. 

  71. <dt><code class="docutils literal notranslate"><span class="pre">omega</span></code></dt><dd><p>the harmonic oscillator angular frequency</p>
    72. 

  72. </dd>
    73. 

  73. </dl>
    74. 

  74. <p>The unit of the returned value matches the unit of hw, since the energy is
    75. 

  75. calculated as:</p>
    76. 

  76. <blockquote>
    77. 

  77. <div><p>E_n = hbar * omega*(n + 1/2)</p>
    78. 

  78. </div></blockquote>
    79. 

  79. <p class="rubric">Examples</p>
    80. 

  80. <div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="kn">from</span> <span class="nn">sympy.physics.qho_1d</span> <span class="kn">import</span> <span class="n">E_n</span>
    81. 

  81. <span class="gp">&gt;&gt;&gt; </span><span class="kn">from</span> <span class="nn">sympy.abc</span> <span class="kn">import</span> <span class="n">x</span><span class="p">,</span> <span class="n">omega</span>
    82. 

  82. <span class="gp">&gt;&gt;&gt; </span><span class="n">E_n</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">omega</span><span class="p">)</span>
    83. 

  83. <span class="go">hbar*omega*(x + 1/2)</span>
    84. 

  84. </pre></div>
    85. 

  85. </div>
    86. 

  86. </dd></dl>
    87. 

  87. 

  88. <dl class="py function">
    89. 

  89. <dt id="sympy.physics.qho_1d.coherent_state">
    90. 

  90. <code class="sig-prename descclassname">sympy.physics.qho_1d.</code><code class="sig-name descname">coherent_state</code><span class="sig-paren">(</span><em class="sig-param"><span class="n">n</span></em>, <em class="sig-param"><span class="n">alpha</span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/sympy/sympy/blob/46469d714a095fde59f9c4d83aaa528c68b0be0f/sympy/physics/qho_1d.py#L67-L78"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#sympy.physics.qho_1d.coherent_state" title="Permalink to this definition"></a></dt>
    91. 

  91. <dd><p>Returns &lt;n|alpha&gt; for the coherent states of 1D harmonic oscillator.
    92. 

  92. See <a class="reference external" href="https://en.wikipedia.org/wiki/Coherent_states">https://en.wikipedia.org/wiki/Coherent_states</a></p>
    93. 

  93. <dl class="simple">
    94. 

  94. <dt><code class="docutils literal notranslate"><span class="pre">n</span></code></dt><dd><p>the “nodal” quantum number</p>
    95. 

  95. </dd>
    96. 

  96. <dt><code class="docutils literal notranslate"><span class="pre">alpha</span></code></dt><dd><p>the eigen value of annihilation operator</p>
    97. 

  97. </dd>
    98. 

  98. </dl>
    99. 

  99. </dd></dl>
    100. 

  100. 

  101. <dl class="py function">
    102. 

  102. <dt id="sympy.physics.qho_1d.psi_n">
    103. 

  103. <code class="sig-prename descclassname">sympy.physics.qho_1d.</code><code class="sig-name descname">psi_n</code><span class="sig-paren">(</span><em class="sig-param"><span class="n">n</span></em>, <em class="sig-param"><span class="n">x</span></em>, <em class="sig-param"><span class="n">m</span></em>, <em class="sig-param"><span class="n">omega</span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/sympy/sympy/blob/46469d714a095fde59f9c4d83aaa528c68b0be0f/sympy/physics/qho_1d.py#L8-L38"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#sympy.physics.qho_1d.psi_n" title="Permalink to this definition"></a></dt>
    104. 

  104. <dd><p>Returns the wavefunction psi_{n} for the One-dimensional harmonic oscillator.</p>
    105. 

  105. <dl class="simple">
    106. 

  106. <dt><code class="docutils literal notranslate"><span class="pre">n</span></code></dt><dd><p>the “nodal” quantum number.  Corresponds to the number of nodes in the
    107. 

  107. wavefunction.  n &gt;= 0</p>
    108. 

  108. </dd>
    109. 

  109. <dt><code class="docutils literal notranslate"><span class="pre">x</span></code></dt><dd><p>x coordinate</p>
    110. 

  110. </dd>
    111. 

  111. <dt><code class="docutils literal notranslate"><span class="pre">m</span></code></dt><dd><p>mass of the particle</p>
    112. 

  112. </dd>
    113. 

  113. <dt><code class="docutils literal notranslate"><span class="pre">omega</span></code></dt><dd><p>angular frequency of the oscillator</p>
    114. 

  114. </dd>
    115. 

  115. </dl>
    116. 

  116. <p class="rubric">Examples</p>
    117. 

  117. <div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="kn">from</span> <span class="nn">sympy.physics.qho_1d</span> <span class="kn">import</span> <span class="n">psi_n</span>
    118. 

  118. <span class="gp">&gt;&gt;&gt; </span><span class="kn">from</span> <span class="nn">sympy.abc</span> <span class="kn">import</span> <span class="n">m</span><span class="p">,</span> <span class="n">x</span><span class="p">,</span> <span class="n">omega</span>
    119. 

  119. <span class="gp">&gt;&gt;&gt; </span><span class="n">psi_n</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="n">x</span><span class="p">,</span> <span class="n">m</span><span class="p">,</span> <span class="n">omega</span><span class="p">)</span>
    120. 

  120. <span class="go">(m*omega)**(1/4)*exp(-m*omega*x**2/(2*hbar))/(hbar**(1/4)*pi**(1/4))</span>
    121. 

  121. </pre></div>
    122. 

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    123. 

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