Lumbar Radiculopathy (Sciatica): This condition is characterized by pain radiating from the lower back down to the feet, often affecting one side of the body. It is commonly caused by a herniated disc, spinal stenosis, or spondylolisthesis, which compresses or irritates the sciatic nerve. The symptoms described, pain from the hip to the feet on one side, align closely with sciatica.

Trochanteric Bursitis: Inflammation of the bursa over the greater trochanter of the femur can cause pain on the outer aspect of the hip, which may radiate down the thigh. While it typically doesn't extend to the feet, it could contribute to hip pain.
Piriformis Syndrome: This condition occurs when the piriformis muscle, which runs from the base of the spine to the thighbone, compresses or irritates the sciatic nerve. It can cause pain in the hip and buttocks that may extend down the back of the leg.
Peripheral Artery Disease (PAD): PAD can cause intermittent claudication, which is pain in the legs or buttocks during exercise that stops when resting. While it typically affects both sides, it could present unilaterally and cause pain from the hip down to the feet.

Cauda Equina Syndrome: A serious condition that occurs when the nerves in the spinal canal are compressed, causing pain, numbness, and weakness in the legs, as well as bladder and bowel dysfunction. It is a medical emergency requiring immediate attention.
Deep Vein Thrombosis (DVT): A blood clot in the deep veins of the legs can cause pain, swelling, and warmth in the affected leg. While it typically doesn't cause hip pain, a large clot could potentially cause referred pain.
Osteonecrosis of the Femoral Head: Also known as avascular necrosis, this condition occurs when there is a loss of blood to the bone tissue, leading to the collapse of the bone. It can cause severe hip pain that may radiate down the leg.

Chronic Regional Pain Syndrome (CRPS): A condition characterized by intense burning or aching pain in the hands or feet after an injury or trauma. It can also affect the legs and is associated with swelling, skin changes, and limited mobility.
Neoplastic Processes: Tumors, either primary or metastatic, affecting the spine, pelvis, or long bones of the leg can cause pain that radiates from the hip to the feet. These are less common but important to consider in the differential diagnosis.
Inflammatory Arthropathies: Conditions like ankylosing spondylitis or psoriatic arthritis can cause hip and leg pain due to inflammation of the spine and joints. While they are less likely to cause unilateral pain from the hip to the feet, they should be considered in patients with a history of inflammatory arthritis.