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Approximation methods are essential tools in quantum mechanics for solving complex physical systems where exact solutions do not exist. This text-only course provides a clear, step-by-step pathway to mastering both the Variational Method and the Wentzel-Kramers-Brillouin (WKB) approximation. By focusing on foundational principles and methodical problem-solving, you will build the confidence needed to tackle exam-style physics questions. You will transition from understanding core mathematical formulations to successfully calculating energy eigenvalues for various potential wells and barriers. This course bridges the gap between abstract quantum theory and practical exam application through detailed written explanations and structured derivations. What you'll learn: - Understand the foundational theory of the Variational Method and the trial wave function selection process. - Calculate upper bounds for ground-state energies of various physical systems. - Apply the WKB approximation method to find energy eigenvalues for symmetric and asymmetric potential wells. - Analyze tunneling probabilities and transmission coefficients through potential barriers. - Practice solving typical exam-level quantum mechanics problems using systematic algebraic steps. - Compare the accuracy of variational results against exact solutions and WKB approximations. The course begins with a thorough introduction to approximation concepts and basic quantum terminology, establishing a solid theoretical foundation. You will then progress through detailed written walkthroughs of the Variational Method, followed by an in-depth study of the WKB approximation and its application to physical potentials. This course is designed for physics students and exam aspirants preparing for advanced competitive tests who have a basic familiarity with introductory quantum mechanics. No prior knowledge of advanced approximation techniques is required. Start mastering these essential quantum approximation methods to boost your exam preparation today.