Histogram line of best fit line is jagged and not smooth?

I can’t quite seem to figue out how to get my curve to be displayed smoothly instead of having so many sharp turns.
I am hoping to show a boltzmann probability distribution. With a nice smooth curve.

I’ll expect it is a simple fix but I can’t see it. Can someone please help?

My code is below:

from matplotlib import pyplot as plt
import numpy as np
import scipy.stats
dE = 1
N = 500
n = 10000

# This is creating an array filled with all twos
def Create_Array(N):
    Particle_State_List_set = np.ones(N, dtype = int)
    Particle_State_List_twos = Particle_State_List_set + 1
    return(Particle_State_List_twos)
Array = Create_Array(N)

def Select_Random_index(N):
    Seed = np.random.default_rng()
    Partcle_Index = Seed.integers(low=0, high= N - 1)
    return(Partcle_Index)

def Exchange(N):
    Particle_Index_A = Select_Random_index(N) #Selects a particle to be used as particle "a"
    Particle_Index_B = Select_Random_index(N) #Selects a particle to be used as particle "b"
    
    # Checks to see if the energy on particle "a" is zero, if so it selects anbother until it isn't. 
    while Array[Particle_Index_A] == 1:
        Particle_Index_A = Select_Random_index(N)
        
     #This loop is making sure that Particle "a" and "b" aren't the same particle, it chooses again until the are diffrent.
    while Particle_Index_B == Particle_Index_A:
        Particle_Index_B = Select_Random_index(N)
        
    # This assignes variables to the chosen particle's energy values
    a = Array[Particle_Index_A]
    b = Array[Particle_Index_B]
    
    # This updates the values of the Energy levels of the interacting particles
    Array[Particle_Index_A] = a - dE  
    Array[Particle_Index_B] = b + dE
   
    return (Array[Particle_Index_A], Array[Particle_Index_B])

for i in range(n):
    Exchange(N)

# This part is making the histogram the curve will be made from
_, bins, _ = plt.hist(Array, 12, density=1, alpha=0.15, color="g")

# This is using scipy to find the mean and standard deviation in order to plot the curve
mean, std = scipy.stats.norm.fit(Array)

# This part is drawing the best fit line, using the established bins value and the std and mean from before
best_fit = scipy.stats.norm.pdf(bins, mean, std)

# Plotting the best fit curve
plt.plot(bins, best_fit, color="r", linewidth=2.5)

#These are instructions on how python with show the graph
plt.title("Boltzmann Probablitly Curve")
plt.xlabel("Energy Value")
plt.ylabel('Percentage at this Energy Value')
plt.tick_params(top=True, right=True)
plt.tick_params(direction='in', length=6, width=1, colors='0')
plt.grid()
plt.show()

Answers:

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Method 1

Whats happening is that in these lines:

best_fit = scipy.stats.norm.pdf(bins, mean, std)
plt.plot(bins, best_fit, color="r", linewidth=2.5)

‘bins’ the histogram bin edges is being used as the x coordinates of the data points forming the best fit line. The resulting plot is jagged because they are so widely spaced. Instead you can define a tighter packed set of x coordinates and use that:

bfX = np.arange(bins[0],bins[-1],.05)
best_fit = scipy.stats.norm.pdf(bfX, mean, std)
plt.plot(bfX, best_fit, color="r", linewidth=2.5)

For me that gives a nice smooth curve, but you can always use a tighter packing than .05 if its not to your liking yet.

All methods was sourced from stackoverflow.com or stackexchange.com, is licensed under cc by-sa 2.5, cc by-sa 3.0 and cc by-sa 4.0