diff --git a/DIRECTORY.md b/DIRECTORY.md
index 150e4e61ea06..49d08edbdb87 100644
--- a/DIRECTORY.md
+++ b/DIRECTORY.md
@@ -242,6 +242,7 @@
     * [Median Two Array](data_structures/arrays/median_two_array.py)
     * [Monotonic Array](data_structures/arrays/monotonic_array.py)
     * [Pairs With Given Sum](data_structures/arrays/pairs_with_given_sum.py)
+    * [Pairwise Iteration](data_structures/arrays/pairwise_iteration.py)
     * [Permutations](data_structures/arrays/permutations.py)
     * [Prefix Sum](data_structures/arrays/prefix_sum.py)
     * [Product Sum](data_structures/arrays/product_sum.py)
@@ -986,6 +987,7 @@
   * [Doppler Frequency](physics/doppler_frequency.py)
   * [Escape Velocity](physics/escape_velocity.py)
   * [Grahams Law](physics/grahams_law.py)
+  * [Hamiltonian](physics/hamiltonian.py)
   * [Horizontal Projectile Motion](physics/horizontal_projectile_motion.py)
   * [Hubble Parameter](physics/hubble_parameter.py)
   * [Ideal Gas Law](physics/ideal_gas_law.py)
diff --git a/data_structures/arrays/pairwise_iteration.py b/data_structures/arrays/pairwise_iteration.py
new file mode 100644
index 000000000000..2efada5c1f39
--- /dev/null
+++ b/data_structures/arrays/pairwise_iteration.py
@@ -0,0 +1,133 @@
+"""
+Author  : Matheus F. Vesco
+Date    : October 3, 2023
+
+Implementation of pairwise iteration algorithms, which can be useful in
+many domains.
+Currently there are two different implementations.
+
+"""
+
+from collections.abc import Iterable, Iterator
+from itertools import tee
+
+
+def pairwise_iteration_tee(iterable: Iterable) -> Iterator[tuple]:
+    """
+    Generate pairs of elements from an iterable.
+
+    This function uses the `tee` function from the `itertools` module to
+    create two independent iterators (`a` and `b`) from the input
+    iterable. The `next` function is used to offset the `b` iterator by
+    one index, and then the two iterators are zipped together to create
+    pairs of elements. This implementation should work with any iterable
+    in Python.
+
+    Args:
+        iterable (Iterable): The input iterable.
+
+    Yields:
+        Iterator[Tuple]: An iterator that yields pairs of objects.
+
+    Examples:
+        >>> list(pairwise_iteration_tee([1, 2, 3]))
+        [(1, 2), (2, 3)]
+
+        >>> list(pairwise_iteration_tee((4, 3, 5)))
+        [(4, 3), (3, 5)]
+
+        >>> list(pairwise_iteration_tee({'x':3, 'y':1, 'z':2, 'foo':4}))
+        [('x', 'y'), ('y', 'z'), ('z', 'foo')]
+
+        >>> list(pairwise_iteration_tee('2345'))
+        [('2', '3'), ('3', '4'), ('4', '5')]
+
+        >>> list(pairwise_iteration_tee(['ATG','GCT','TGC','TAA']))
+        [('ATG', 'GCT'), ('GCT', 'TGC'), ('TGC', 'TAA')]
+
+        >>> list(pairwise_iteration_tee(['a']))
+        []
+    """
+    # Uses itertools.tee to create two independent iterators (a and b)
+    # from the iterable. This means we can use next() on each one
+    # without affecting the other, no matter the iterable type
+    a, b = tee(iterable)
+
+    # Offsets the second iterator (b) by one step to create a staggered
+    # alignment.
+    # this means that (a[i],b[i]) represents the same as (a[i],a[i+1])
+    next(b, None)
+
+    # Returns a zip generator that pairs items from the two iterators in
+    # the format (a[i], a[i+1]).
+    return zip(a, b)
+
+
+def pairwise_iteration_comprehension(
+    iterable: Iterable, step: int = 1
+) -> Iterator[tuple]:
+    """
+    Generate pairs of elements from an iterable with a given step size.
+
+    This function uses list comprehensions to get the items that are step
+    distance from each other and later the `iter()` conversion to create
+    two independent list iterators (`a` and `b`) from the input iterable.
+    The `next` function is used to offset the `b` iterator by one index,
+    and then the two iterators are zipped together to create pairs of
+    elements.
+
+    Args:
+        iterable (Iterable): The input iterable.
+        step (int, optional): The step size for iterating through the
+        input iterable. Defaults to 1.
+
+    Yields:
+        Iterator[Tuple]: An iterator that yields pairs of objects.
+
+    Examples:
+        >>> list(pairwise_iteration_comprehension([0, 1, 2, 3, 4, 5, 6], step=2))
+        [(0, 2), (2, 4), (4, 6)]
+
+        >>> list(pairwise_iteration_comprehension([0, 1, 2, 3, 4, 5, 6], step=3))
+        [(0, 3), (3, 6)]
+
+        >>> list(pairwise_iteration_comprehension((0, 1, 2, 3, 4), step=2))
+        [(0, 2), (2, 4)]
+
+        >>> python_set = pairwise_iteration_comprehension(
+        ...     {4, 3, 2, 1, 0}, step=2)
+        >>> list(python_set) # sets are unordered
+        [(0, 2), (2, 4)]
+
+        >>> dictionary = pairwise_iteration_comprehension(
+        ...     {'x1':4, 'y1':5, 'x2':1, 'y2':'a', 'spam':7}, step=2)
+        >>> list(dictionary)
+        [('x1', 'x2'), ('x2', 'spam')]
+
+        >>> list(pairwise_iteration_comprehension({0, 1, 2, 3, 4, 5, 6}, step=3))
+        [(0, 3), (3, 6)]
+
+        >>> list(pairwise_iteration_comprehension(['ATG','GCT','TGC','TAA']))
+        [('ATG', 'GCT'), ('GCT', 'TGC'), ('TGC', 'TAA')]
+
+        >>> list(pairwise_iteration_comprehension(['a'], step=1))
+        []
+    """
+    # creates a list, using list comprehensions, that only stores items
+    # that are n steps apart from each other.
+    items = [item for i, item in enumerate(iterable) if i % step == 0]
+
+    # creates two independent list iterators (a and b) from the list
+    # we created earlier, using the iter() function. This means we can
+    # use next() on each one without affecting the other, no matter the
+    # iterable type
+    a, b = (iter(items), iter(items))
+
+    # Offsets the second iterator (b) by one step to create a staggered
+    # alignment.
+    # this means that (a[i],b[i]) represents the same as (a[i],a[i+1])
+    next(b, None)
+
+    # Returns a zip generator that pairs items from the two iterators in
+    # the format (a[i], a[i+1]).
+    return zip(a, b)