Transparent Corp's Research Area is arguably the most comprehensive resource for collated brainwave entrainment research. Update: the main research area on Transparent Corp's website is currently being updated, so it is offline. However, you can still access their peer-reviewed research paper as a PDF here: “A Comprehensive Review of the Psychological Effects of Brainwave Entrainment“.
All techniques, whether mantra, focus on the breath, contemplation of a koan, or any other, are simply the vehicles we use to take us into (hopefully) a meditative state. Put another way, the purpose of repeating a mantra is not to get proficient at repeating a mantra. The purpose is to take us to a meditative state where the mantra slips away and is no longer necessary.
Your brainwave activity during sleep is largely distinct from your brain activity when you’re awake. (REM sleep is one exception to this—during REM, your brain is active in ways very much like when you’re awake.) During non-REM sleep, the slower, lower frequency theta and delta waves dominate, compared to the alpha and beta waves that are prominent when you’re alert and active.
Theta is very subtle. It is one of the most elusive and extraordinary brain states you can explore. Theta is a state of somnolence with reduced consciousness; you are neither fully awake nor asleep yet. It is also known as the “Twilight state” or “Stage 1 Sleep” which you normally only experience fleetingly as you wake or drift off to sleep. In the Theta brain state, your senses are withdrawn from the external world and focused on signals originating from within.
Theta brain waves occur most often in sleep but are also dominant in deep meditation. Theta is known to be a dreamlike state with vivid imagery, intuition and information beyond your normal conscious awareness. This state of mind is excellent for psychic experiences to occur, as well as astral projection and extended remote viewing. To reach this state without falling asleep while meditating takes practice.
Most capsules either contain powdered, dry herbs, or a tiny bit of liquid extract (gel caps). Tablets are powdered herbs that are held together by pressure and other chemicals. The beauty of liquid extracts, or "tinctures," is that they absorb quickly and the body receives the full benefit of the plant in a very bio-available solution. Liquids also allow you to customize your serving freely so you can best meet your needs at the time. Liquids are inexpensive and easy to swallow. The droppers and pump top dispensers are also convenient for when you're on the go.
Brainwave entrainment music can be used almost anywhere and anytime, making this mood and self-improvement method versatile and flexible enough to do at work, while traveling, or at other times during the day. When used in the workplace during short rest periods, brainwave entrainment techniques can enhance concentration, communication, and work productivity.
Both brainwave entrainment and neurofeedback deal with brainwaves, but the similarity stops there. Entrainment pushes your whole brain into a pre-determined state, while neurofeedback teaches you how to move specific parts of your brain on your own. It is the differeence between forcing the brain into a given position, and skills building so you can move it there yourself.