#!/usr/bin/env python
# coding: utf-8

# # QuTiP example: eseries

# J.R. Johansson and P.D. Nation
# 
# For more information about QuTiP see [http://qutip.org](http://qutip.org)

# In[1]:


from numpy import pi


# In[2]:


from qutip import *


# ## Example eseries object: $\sigma_x  \exp(i\omega t)$

# In[3]:


omega = 1.0
es1 = eseries(sigmax(), 1j * omega)


# In[4]:


es1


# ## Example eseries object: $\sigma_x \cos(\omega t)$

# In[5]:


omega = 1.0
es2 = eseries(0.5 * sigmax(), 1j * omega) + eseries(0.5 * sigmax(), -1j * omega)


# In[6]:


es2


# ## Evaluate eseries object at time $t = 0$

# In[7]:


esval(es2, 0.0)


# ## Evaluate eseries object at array of times $t = [0, \pi, 2\pi]$

# In[8]:


tlist = [0.0, 1.0 * pi, 2.0 * pi]
esval(es2, tlist)


# ## Expectation values of eseries

# In[9]:


es2


# In[10]:


expect(sigmax(), es2)


# ## Arithmetics with eseries

# In[11]:


es1 = eseries(sigmax(), 1j * omega)
es1


# In[12]:


es2 = eseries(sigmax(), -1j * omega)
es2


# In[13]:


es1 + es2


# In[14]:


es1 - es2


# In[15]:


es1 * es2


# In[16]:


(es1 + es2) * (es1 - es2)


# ## Expectation values of eseries

# In[17]:


es3 = eseries([0.5*sigmaz(), 0.5*sigmaz()], [1j, -1j]) + eseries([-0.5j*sigmax(), 
                                                                  0.5j*sigmax()], [1j, -1j])
es3


# In[18]:


es3.value(0.0)


# In[19]:


es3.value(pi/2)


# In[20]:


rho = fock_dm(2, 1)
es3_expect = expect(rho, es3)

es3_expect


# In[21]:


es3_expect.value([0.0, pi/2])


# ## Versions

# In[22]:


from qutip.ipynbtools import version_table

version_table()