Accurate sleep stage classification based on single-channel electroencephalogram (EEG) signals remains a fundamental challenge in automated sleep staging. Existing deep learning architectures may be limited by fixed receptive fields, sequential processing bottlenecks, and inadequate adaptation to inter-subject variability. We propose an Adaptive Multi Scale Temporal-Spectral Network (AMT-SNet) designed for efficient and accurate single-channel EEG-based sleep stage classification. Our method employs a dual-branch architecture with temporal-spectral feature extraction, subject-adaptive calibration, and component-wise training to achieve robust and personalized sleep stage classification. We evaluated our method on the Sleep-EDF-20 dataset for five-class sleep stage classification and further validated its generalization ability using the Sleep-EDF-78 dataset. The results on the Sleep-EDF-20 dataset demonstrate that AMT-SNet outperforms eight state-of-the-art models, achieving an accuracy of 85.8% and a macro F1-score of 79.4%. Furthermore, it exhibits strong generalization capability on the Sleep-EDF-78 dataset, setting new performance benchmarks for automated single-channel sleep stage classification. In summary, AMT-SNet offers an effective and generalizable approach for accurate and personalized single-channel sleep stage classification.