<p>This paper presents a detailed study of wave packets on the Heisenberg group <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\({\mathbb {H}}^n,\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msup> <mrow> <mi mathvariant="double-struck">H</mi> </mrow> <mi>n</mi> </msup> <mo>,</mo> </mrow> </math></EquationSource> </InlineEquation> a fundamental non-commutative Lie group arising naturally in harmonic analysis and quantum mechanics. We develop the theory of wave packet transforms adapted to the intrinsic geometry and representation theory of <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\({\mathbb {H}}^n.\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msup> <mrow> <mi mathvariant="double-struck">H</mi> </mrow> <mi>n</mi> </msup> <mo>.</mo> </mrow> </math></EquationSource> </InlineEquation> Key contributions include the characterization of admissible wave packets, the construction of continuous frames generated by dilations, modulations, and translations on <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\({\mathbb {H}}^n,\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msup> <mrow> <mi mathvariant="double-struck">H</mi> </mrow> <mi>n</mi> </msup> <mo>,</mo> </mrow> </math></EquationSource> </InlineEquation> and explicit inversion formulas using dual frames. We provide explicit examples of admissible wave packets arising from Gaussian-type functions and heat kernels, emphasizing their localization and spectral properties. The results establish a robust framework for time-frequency analysis on <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\({\mathbb {H}}^n\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mrow> <mi mathvariant="double-struck">H</mi> </mrow> <mi>n</mi> </msup> </math></EquationSource> </InlineEquation> and open pathways for applications in signal processing and partial differential equations on non-commutative groups.</p>