Plotting Quantum Harmonic Oscillator in Mathematica
How can I make the plot for quantum harmonic oscillator using Mathematica? I would like to draw similar looking plot like the attached figure.
Solution
Energy[n_] := (2 n + 1) ℏ/2 ω;
ψ[z_, n_] :=
1/2 1/Sqrt[2^n n!] ((m ω)/(π ℏ))^(1/4)
Exp[-((m ω z^2)/(2 ℏ))] HermiteH[n, Sqrt[(m ω)/ℏ] z];
m = 1;
ω = 1;
ℏ = UnitConvert[Quantity[1, "PlanckConstant"], "SIBase"];
ℏ = QuantityMagnitude[ℏ];
ℏ = 1;
Plot[{Evaluate@Table[Energy[n] + ψ[z, n], {n, 0, 5}],
Evaluate@Table[Energy[n], {n, 0, 5}], z^2/2}, {z, -5, 5},
PlotRange -> {0, 7},
PlotStyle ->
Join[{Red, Yellow, Green, Blue, Purple, Cyan},
Table[{Gray, Opacity[0.3]}, {n, 0, 5}], {Black}],
Filling -> {1 -> Energy[0], 2 -> Energy[1]}]
- Transform slider linear values to exponent
- Evaluating a string as a mathematical expression in JavaScript
- Calculate rotation to have div in "front" when parent container is rotated (Solved)
- complex multiplication / divison with infinity and nan
- How did Python implement the built-in function pow()?
- Python and Powers Math
- GPS coordinates: 1km square around a point
- How to check if a number is a power of 2
- Why does Math.Sign() throws exception when passed a NaN?
- How does java do modulus calculations with negative numbers?
- Finding the string length of a integer in .NET
- LeetCode 231: Problem in finding whether a given number is Power of 2
- What is the remainder of integer division?
- Is floating-point math broken?
- Is there a difference between scipy.pi, numpy.pi, or math.pi?
- How to prove that "i & (i - 1) == 0" means "i is the power of 2"
- Efficient implementation of natural logarithm (ln) and exponentiation
- How can I simulate firefox animation behaviour on chrome when using calcMode="linear"?
- How to get ceil value of number when divided in <s:iterator> tag in Struts 2
- How does this bitwise operation check for a power of 2?
- Why are mathematical constants truncated differently in powershell?
- Using bitwise operators on > 32 bit integers
- Constraining a number to a looping range. Is there a more elegant function?
- Why is the counter decrementing correctly but the countdown is not?
- Math question in regards to functions in the form (1) / ( b ^ c )
- calculate shift hours with break time deductions starting from current night to next day morning using google apps script
- Denormalizing thetas after a linear regression with gradient descent
- How to calculate percentage when old value is ZERO
- Intuitive Understanding of GCD algorithm
- What's the simplest way to extend a numpy array in 2 dimensions?